Solving the provided question, we cans say that by quadratic equation, the age where a person's systolic pressure is 127.54 mm Hg is 46
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared.
systolic pressure for a person of age 45 years, just plug in y = 45:
systolic pressure is 127.54 mm Hg, plug in P = 127.54
P = 0.004y2 - 0.02y + 120
127.54 = 0.004y2 - 0.02y + 120
0 = 0.004y2 - 0.02y - 7.54
Use the quadratic formula to solve this. The quadratic formula (for ay2 + by + c = 0) is:
y = [-b ± √(b2 - 4ac)]/(2a)
In this case a = 0.004, b = - 0.02 and c = - 7.54 so:
[tex]y = [-b + \sqrt{(b2 - 4ac)]/(2a)}\\y = [-(-0.02) +\sqrt{((0.02)2 - 4(0.004)(-7.54))]/(2(0.004))}\\y = [0.02 + \sqrt{(0.0004 + 0.12064)]/0.008}\\y = [0.02 + \sqrt{0.12104]/0.008}\\y = [0.02+ 0.3479]/0.008\\ y = [0.02 + 0.3479]/0.008 or y = 0.3679/0.008 = 45.989\\ y = [0.02 - 0.3479]/0.008 or y = -0.3279/0.008 = -40.989\\[/tex]
Since -40.988 makes no sense (40.989 years before birth), we throw that answer out.
The age where a person's systolic pressure is 127.54 mm Hg is 46
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Which table shows a proportional relationship between x and y?
From the given tables, Tables 2 and 3 will show the proportional relationship between x and y.
What is Proportionality:Two ratios or two fractions are comparable according to the equation of proportion. In other words, when two ratios are equal, they are said to be proportionate.
Let x and y be proportional relation
=> x ∝ y
=> x = ky
=> x/y = k [ where 'k' proportionality constant ]
Here we have
Table 1
x 2 3 4 5
y 7 9 11 13
=> [tex]\frac{x}{y} = \frac{3}{7} = \frac{3}{9}[/tex] [ which is not true ]
Hence,
Table 1 not shows any proportional relationship between x and y
Table 2
x 3 7.5 15 25
y 1 2.5 4 6
=> [tex]\frac{x}{y} = \frac{3}{1} = \frac{7.5}{2.5} = 3[/tex] [ which is true ]
Hence, Table 2, shows a proportional relationship between x and y
Table 3
x 1 2 7 8
y 0.5 1 3.5 4
=> [tex]\frac{x}{y} = \frac{1}{0.5} = \frac{2}{1} = 2[/tex] [ Which is true ]
Hence, Table 3 shows a proportional relationship between x and y
Table 4
x 3 6 8 10
y 12 15 18 20
=> [tex]\frac{x}{y} = \frac{3}{12} = \frac{6}{15}[/tex] [ Which is not true ]
Hence, Table 4 not shows a proportional relationship between x and y
Therefore,
From the given tables, Tables 2 and 3 will show the proportional relationship between x and y.
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.A certain store is selling packages of 10 pencils and 4 pens for back to school. The store manag wants to make a larger package in the same ratio. If the large package has 10 pens, how mar pencils are in the large package?
Answer:
4 pencils.
Step-by-step explanation:
The ratio of pencils to pens in the original package is 10:4, which means that for every 4 pens, there are 10 pencils. To find the number of pencils in the larger package, we can use this same ratio.
If the large package has 10 pens, we can set up the proportion:
x/10 = 10/4
Where x is the number of pencils in the large package. To solve for x, we can cross-multiply:
10 * 4 = x * 10
40 = x*10
x = 40/10
x = 4
So the large package contains 4 pencils.
Question
A proposed change in income tax suggests charging 20% on a person's income up to $30, 000 and then 40% on any
income above that. If a person has an income of $47, 000, what will be their income tax under the proposal?
Give your answer in dollars to the nearest dollar. Do not include commas or the dollar symbol in your answer.
The total income tax imposed on $47,000 is $12,800
How does income tax work?The term "income tax" describes a class of taxes that governments impose on income generated by people and businesses within their territorial jurisdiction.
Taxpayers are required by law to submit an income tax return each year in order to determine their tax obligations.
Income taxes are the main source of funding for governments. They are employed to fund public services, provide residents with goods, and settle debts owing to the government.
A number of states and municipal governments, in addition to the federal government, also require payment of income tax. The Internal Revenue Service is responsible for collecting taxes and enforcing the tax laws in the United States (IRS).
Regarding credits, deductions, and other forms of taxable and reportable income.
Firstly let us break the income tax as per the given condition
Income = 47,000 = 30,000 + 17,000
hence 20% tax is imposed on $30,000 and 40% on $17,000
Total income tax = 20% of 30000 + 40% of 17000
Total income tax = 6000 + 6800 = 12800
hence, The total income tax imposed on $47,000 is $12,800.
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what percent of 40 is 50?
Answer:20
Step-by-step explanation:
Answer:
the percent of 40 is 50
the answer to this is 10
6. Find m4V.
Y
V
(10x-27)
(2x +29)
X
W
nswers 1-7
Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.
what is angles ?In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that come together at a point in the middle known as the angle's vertex. An angle that is in the plane where the rays are placed can be created by two rays. An angle is also produced when two planes collide. They are known as dihedral angles. In planar geometry, an angle is the form produced by two rays or lines that share a termination. The English word "angle" comes from the Latin word "angulus," which means "horn." The vertex, also known as the sides of the angle, is where the two rays' common terminals meet.
given
m∠V + m∠W + m∠X + m∠Y = 360
10x -27 + 2x + 19 = 180
12x - 8 = 180
188 = 12x
x = 15.66
m∠V + m∠X = 180
2x = 180
x = 90
Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.
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Solve for x. -3x - 6 = -4x + 5
The solution to the equation -3x - 6 = -4x + 5 is x = 11.
What is equation?
An equation is a mathematical statement that uses an equals sign (=) to show that two expressions have the same value.
To solve for x in the equation -3x - 6 = -4x + 5, we need to isolate the variable x on one side of the equation. We can do this by adding 4x to both sides of the equation to eliminate the negative 4x term on the right-hand side:
-3x - 6 + 4x = -4x + 5 + 4x
Simplifying the left-hand side by combining like terms, we get:
x - 6 = 5
Finally, to isolate x, we add 6 to both sides of the equation:
x - 6 + 6 = 5 + 6
Simplifying the left-hand side and the right-hand side, we get:
x = 11
Therefore, the solution to the equation -3x - 6 = -4x + 5 is x = 11.
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Need answer quick 100 points! and brainliest
Graph using this picture
y+4=2/5(x−3)
Answer:
See attached graph.
Step-by-step explanation:
Given equation:
[tex]y+4=\dfrac{2}{5}(x-3)[/tex]
Expand the right side of the equation:
[tex]\implies y+4=\dfrac{2}{5}x-\dfrac{6}{5}[/tex]
Subtract 4 from both sides of the equation:
[tex]\implies y=\dfrac{2}{5}x-\dfrac{26}{5}[/tex]
Substitute x = 3 into the equation:
[tex]\implies y=\dfrac{2}{5}(3)-\dfrac{26}{5}[/tex]
[tex]\implies y=\dfrac{6}{5}-\dfrac{26}{5}[/tex]
[tex]\implies y=-\dfrac{20}{5}[/tex]
[tex]\implies y=-4[/tex]
Substitute x = -2 into the equation:
[tex]\implies y=\dfrac{2}{5}(-2)-\dfrac{26}{5}[/tex]
[tex]\implies y=-\dfrac{4}{5}-\dfrac{26}{5}[/tex]
[tex]\implies y=-\dfrac{30}{5}[/tex]
[tex]\implies y=-6[/tex]
To graph the given equation, plot the two found points on the given coordinate plane:
(3, -4)(-2, -6)Draw a straight line through the points.
(See attachment).
Chris is employed as a waiter in an upscale
restaurant. His restaurant pays him $5.75 per hour
during which time he can serve two groups. The
average tip per group is $8.75. Write an equation that
outputs Chris' total income (1) based on the number of
hours he works (h).
Equation that represents Chris's total income = ($5.75+$17.5) X, where X is the number of hours he works in a day.
What is equation?Equation is a mathematical statement that expresses the equality between two or more expressions.
Equation are different types such as equation with one variables and equation with two variables. The equation is used to determine the unknown values.
What is the equation that outputs Chris total income?Assume, Chris works X hours in a day.
He earns $5.75 per hour.
during his work time he serves two groups.
The average tip per group = $8.75
tips earned from two groups = $8.75 × 2 = $17.5
Outputs of Chris total income if he works total X hours in a day
= ($5.75+$17.5) X
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What is the quotient of -231 and 3
Answer :-77. ✅
Step-by-step explanation:
To find the quotient of -231 and 3, we divide -231 by 3.
-231 ÷ 3 = -77
The quotient of -231 and 3 is ✅
Which shows the pre-image of triangle XYZ' before the figure was rotated 90° about the origin?
Answer: 2nd picture
Step-by-step explanation: its rotating 90 degrees
Question 8(Multiple Choice Worth 2 points) (Laws of Exponents with Whole Number Exponents LC) Which is an equivalent expression for (52 • 34)3?
Answer:
An equivalent expression for (52 • 34)3 would be (52 • 34) • (52 • 34) • (52 • 34)
Another way to express this is (52)3 • (34)3
So it can also be written as (5^32^3) * (3^44^3)
It can be also expressed as 125 * (81*64)
This expression is the result of multiplying three times the product of 5^2 and 3^4
This system of linear inequalities can be used to find the possible heights, in inches, of Darius, d, and his brother William, w.
d ≥ 36
w < 68
d ≤ 4 + 2w
Which statements must be true about their heights? Select three options.
Darius is at least 36 inches tall.
Darius is at most 36 inches tall.
William’s height is less than 68 inches.
William’s height is at least 68 inches.
Darius is less than 4 inches taller than twice William’s height.
Darius is no more than 4 inches taller than twice William’s height.
Since this system of linear inequalities can be used to find the possible heights, in inches, of Darius, d, and his brother William, w, the three statements which must be true about their heights include all of the following:
A. Darius is at least 36 inches tall.
C. William’s height is less than 68 inches.
F. Darius is no more than 4 inches taller than twice William’s height.
How to write and interpret the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the possible heights, in inches, for Darius and Williams, and then translate the word problem into algebraic equation as follows:
Let the variable d represent the Darius's height.Let the variable w represent the number of William’s height.Next, we would interpret the given system of linear inequalities as follows;
d ≥ 36 ⇒ "Darius is at least 36 inches tall." because of the greater than or equal to (≥) inequality symbol.
w < 68 ⇒ "William’s height is less than 68 inches." because of the less than (<) to inequality symbol.
Additionally, d ≤ 4 + 2w ⇒ "Darius is no more than 4 inches taller than twice William’s height." because of the less than or equal to (≤) inequality symbol.
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Write an equation that represents the line.
Use exact numbers.
Please help quickly!! my test is due soon!!
On solving the provided question, we can say that from the given graph, it is shown that it is a starlight line so the equation that represents is x = y => x-y = 0
What is graphs?Mathematicians use graphs to logically convey facts or values using the visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
here, from the given graph
it is shown that it is a starlight line
so the equation that represents is x = y
x-y = 0
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(1,-9) and (-3,-9) in slope intrcept form
Multi-Step Linear Equations LC)
Solve −7x− 7 = −3x + 9 for x.
A: x = −4
B: x = −3
C: x = 3
D: x = 4
Answer:
A) x= -4
Step-by-step explanation:
-7x+3x=7+9
-4x= 16
x= 16÷ -4 = -4
HELPPPP ASAPPPP!!!!
Solve:
2x-10
———- = 3x
4
X = -10
X = -1
x = 2
X = 11
The solution of this equation is given by x = -10 ( option A)
What is an equation ?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.
The equation is
2x - 10 = 3x
⇒ x = -10
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4x = 8x − 1 (5 points) x = three fourths x = 1 x = 3 x = 6
For expression 4x=8x-1, x will be 1/4.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
As given expression is 4x=8x-1
8x-4x=1
4x=1
x=1/4
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Darby has a $50 gift card to spend at a coffee shop. Each cup of coffee is $2.40. Write and solve an inequality to determine how many cups of coffee she can buy so she has at least $8 left to purchase an insulated mug.
Question: Darby has a $50 gift card to spend at a coffee shop. Each cup of coffee is $2.40. Write and solve an inequality to determine how many cups of coffee she can buy so she has at least $8 left to purchase an insulated mug.
To make an equation we need to do $50-$8 to see how much money we have left to spend on coffee after buying the mug which is $42
42 divided by 2.4 = 17.5 but since you cant buy half a coffee you’d get 17 with $1.2o left over
A way to write this equation is 2.4C + 8 = 50
C acts as a variable to represent the number of cups of coffee you can get while 8 just stands for the one insulated mug you want
hope this helps :D
Answer: 2.4C + 8 = 50
A professional basketball player is 76 inches tall. A model of this player is 6
inches tall. Determine the simplified scale factor of the model to the real-life
player. Use colon notation. Then explain what the scale factor means.
The scale factor of the model to the real-life player is 6:76. This can be read as 6/76 or 0.0789 or 0.079(approximately)
The scale factor is a ratio that compares the size of the model to the size of the real-life object. In this case, the scale factor of 6:76 tells us that for every 76 inches of the real-life player, the model is only 6 inches. In other words, the model is 6/76 or approximately 0.0789 times smaller than the real-life player.
In general, a scale factor is a number used to multiply all the dimensions of an object to get a corresponding model or representation of that object, where the ratio of the corresponding dimensions between the real-life object and the model is represented by the scale factor.
It should be noted that the scale factor can also be represented in fraction or decimal form, but the colon notation gives a more meaningful representation of the comparison of the size between the model and the real-life object.
Answer: The scale factor for the basketball player to the model is 16 inches to 1 inch
Step-by-step explanation:
or
A French restaurant used 203,640 ounces of cream last year. This year, due to a menu update, it used 65% less. How much cream did the restaurant use this year?
This year 71, 274 ounce cream used.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
A French restaurant used 203,640 ounces of cream last year.
This, year 65% less cream used.
So, this year the amount of cream used
= 203640 - 203640 x 65%
= 203640 - 203640 x 0.65
= 203640 - 132366
= 71274 ounce
Hence, 71274 ounce cream used this year.
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Suppose the set A = U. How many elements are [tex]A^{c}[/tex]
The number of elements in [tex]A^c[/tex] is zero.
What is a set?A set is a collection of items where there are operations such as:
Union of sets, the intersection of sets, and the complement of sets.
We have,
U = universal set
This includes all values.
[tex]A^c[/tex] = complement of set A.
This means,
All the elements of U except the elements of A.
[tex]A^c[/tex] = U - A
Now,
If A = U,
[tex]A^c[/tex] = U - U = 0
Thus,
There are no elements in [tex]A^c[/tex].
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Alex is purchasing 3 concert tickets. The website charges a $5 fee for each ticket. Her total is $117. What is the original cost of each concert ticket? Choose the equation that represents the situation.
The original cost for each concert ticket is given as follows:
$34.
How to obtain the original cost for each concert ticket?The original cost for each concert ticket is obtained applying the proportions in the context of this problem.
The fee for a single ticket is divided as follows:
$5 fee for the website.$n fee for the original cost.Hence the proportional relationship that models the cost of purchasing x tickets is given as follows:
y = (5 + n)x.
Alex purchased 3 concert tickets, meaning that x = 3, for a total of $117, meaning that y = 117, hence the original cost n is obtained as follows:
117 = (5 + n) x 3
Dividing by 3 on both sides, we have that:
5 + n = 39
n = 39 - 5
n = $34.
Which is the original cost for each concert ticket.
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Use the figure to the right to find the value of PT. T is the midpoint of PQ.
PT=3x+6 and TQ=5x-6
The value of the variable 'x' is 6. Then the length of the line segment PT will be 24 units.
What is a line segment?A line segment in mathematics has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a path that joins two places.
The information is given below.
PT = 3x + 6 and TQ = 5x - 6
T is the midpoint of PQ. Then the equation is given as,
PT = TQ
3x + 6 = 5x - 6
2x = 12
x = 6
Then the length of the line segment PT will be given as,
PT = 3(6) + 6
PT = 18 + 6
PT = 24 units
The value of the variable 'x' is 6. Then the length of the line segment PT will be 24 units.
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Use the table to write a linear function that relates y to x
Answer:
From the table, we can see that the y value is always -7, regardless of the x value. This means that the y-intercept of the function is -7.
Step-by-step explanation:
From the table, we can see that the y value is always -7, regardless of the x value. This means that the y-intercept of the function is -7.
Therefore, the linear function that relates y to x, using this table, is:
y = -7
It's a constant function, no matter what the x value is, the y value is always -7.
Sam is renting one of two cars to go on a 300 mile trip. The first car can travel 75 miles on 5 gallons of gas. The second car can travel 240 miles on a 20 gallons of gas. Each car costs the same to rent. And Sam wants to rent the car with better gas mileage. Sam estimate that he will pay 49.42 for every 14 gallons of gas he has to buy. Which car should Sam rent, and how much money should Sam bring for gas?
The better car is car A and Sam would pay $70.
Which car is better?We can see that we can only be able to judge the better car by the way that the gas is able to consume fuel. We can now see that the cars are two and we have the gas consumption of each as;
For car A = 75 miles / 5 gallons = 15 miles/gallon
For car B = 240 miles/ 20 gallons = 12 miles/gallon
As such car A is the better car.
Miles to be covered = 300 miles
If 1 gallon takes 15 miles
x galloons takes 300 miles
x = 20 gallons
If 14 gallons cost $49.42
1 gallon costs 49.42/14
=$3.5
Sam would pay; $3.5 * 20
= $70
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400 divide by 15=_ divide by 1/2
Answer:
53.333
Step-by-step explanation:
400/15 x 2 = 53.333
(Multiplying Linear Expressions MC)
Multiply 5c(9 − 4c).
A: 45c − 4c
B: 45c − 20c2
C: 45c − 20c
D: 45 − 20c2
Answer:
45c-20c²
Step-by-step explanation:
You just multiply the number outside the bracets with the numbers inside.
5c×9= 45c
5c×-4c= -20c²
So the answer is 45c-20c²
Which is option 'B'
Which graph represents the solution to the following sentence?
{x\x>4} U {x|x < -2}
-3 -2 -1 0 1 2345
-4 -3 -2 -1 0 1 2 3 4
-3 -2 -1 0 1 2 3 4 5
Answer: The graph represents the solution to the following sentence is the option number 3:
-3 -2 -1 0 1 2 3 4 5
This is because the set notation {x|x>4} U {x|x<-2} represents the union of all values of x that are greater than 4 and all values of x that are less than -2. The graph shows all the values of x that are greater than 4 and all values of x that are less than -2. The graph also includes the values of x between -3 and 5, it encompasses all the values that are greater than 4 and all values that are less than -2.
The graph represents the solution to the following sentence is (C).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We have,
{x | x >4 } ∪ {x | x < -2}
Here the set notation {x|x>4} U {x|x<-2} represents the union of all values of x that are greater than 4 and all values of x that are less than -2.
The graph displays all instances of x larger than 4 and all instances of x less than -2.
The graph covers all x values higher than or equal to 4, as well as all x values less than or equal to -2.
It also includes x values between -3 and 5.
Thus, the number line is C.
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13. Translate to an algebraic expression.
The result of subtracting j from 13
The algebraic expression for "the result of subtracting j from 13" can be written as 13 - j.
How do you construct an algebraic expression for subtraction?The signs of all the terms in the algebraic expression that is to be subtracted from another must be changed from "+" to "-" or from "-" to "+" before the two expressions are added.In algebra, subtraction is an operation that can be used to determine the difference between two numbers. Subtraction is represented by the minus sign (-).When subtracting, the number being subtracted from is called the minuend, and the number being subtracted is called the subtrahend. To subtract j from 13, the minuend is 13, and the subtrahend is j.Therefore, the algebraic expression for "the result of subtracting j from 13" can be written as 13 - j.Subtraction is a fundamental operation in algebra which can be used to solve many types of problems.It can be used to determine the difference between two numbers, as well as to solve equations.For example, if the equation 5x - j = 13 is given, we can use subtraction to solve for x.To do this, we would subtract j from both sides of the equation, resulting in the equation 5x = 13 - j.We can then divide both sides by 5 to get x = (13 - j) / 5. Therefore, the result of subtracting j from 13 is (13 - j).
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Write the solution of the inequality in set-builder notation:
NEED HELP ASAP
The solution of the inequality in set-builder notation is {p I p ≥ 1}.
The correct option is A.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
An inequality,
2(3p-11) ≥ -16
Solving the parenthesis,
6p-22 ≥ -16
6p ≥ -16 + 22
6p ≥ 6
p ≥ 1
Therefore, the solution is {p I p ≥ 1}.
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