# 2.7 Solve linear inequalities  (Page 7/8)

 Page 7 / 8

## Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

## Section 2.1 Solve Equations using the Subtraction and Addition Properties of Equality

Verify a Solution of an Equation

In the following exercises, determine whether each number is a solution to the equation.

$10x-1=5x;x=\frac{1}{5}$

$w+2=\frac{5}{8};w=\frac{3}{8}$

no

$-12n+5=8n;n=-\frac{5}{4}$

$6a-3=-7a,a=\frac{3}{13}$

yes

Solve Equations using the Subtraction and Addition Properties of Equality

In the following exercises, solve each equation using the Subtraction Property of Equality.

$x+7=19$

$y+2=-6$

$y=-8$

$a+\frac{1}{3}=\frac{5}{3}$

$n+3.6=5.1$

$n=1.5$

In the following exercises, solve each equation using the Addition Property of Equality.

$u-7=10$

$x-9=-4$

$x=5$

$c-\frac{3}{11}=\frac{9}{11}$

$p-4.8=14$

$p=18.8$

In the following exercises, solve each equation.

$n-12=32$

$y+16=-9$

$y=-25$

$f+\frac{2}{3}=4$

$d-3.9=8.2$

$d=12.1$

Solve Equations That Require Simplification

In the following exercises, solve each equation.

$y+8-15=-3$

$7x+10-6x+3=5$

$x=-8$

$6\left(n-1\right)-5n=-14$

$8\left(3p+5\right)-23\left(p-1\right)=35$

$p=-28$

Translate to an Equation and Solve

In the following exercises, translate each English sentence into an algebraic equation and then solve it.

The sum of $-6$ and $m$ is 25.

Four less than $n$ is 13.

$n-4=13;n=17$

Translate and Solve Applications

In the following exercises, translate into an algebraic equation and solve.

Rochelle’s daughter is 11 years old. Her son is 3 years younger. How old is her son?

Tan weighs 146 pounds. Minh weighs 15 pounds more than Tan. How much does Minh weigh?

161 pounds

Peter paid $9.75 to go to the movies, which was$46.25 less than he paid to go to a concert. How much did he pay for the concert?

Elissa earned $152.84 this week, which was$21.65 more than she earned last week. How much did she earn last week?

$131.19 ## Section 2.2 Solve Equations using the Division and Multiplication Properties of Equality Solve Equations Using the Division and Multiplication Properties of Equality In the following exercises, solve each equation using the division and multiplication properties of equality and check the solution. $8x=72$ $13a=-65$ $a=-5$ $0.25p=5.25$ $\text{−}y=4$ $y=-4$ $\frac{n}{6}=18$ $\frac{y}{-10}=30$ $y=-300$ $36=\frac{3}{4}x$ $\frac{5}{8}u=\frac{15}{16}$ $u=\frac{3}{2}$ $-18m=-72$ $\frac{c}{9}=36$ $c=324$ $0.45x=6.75$ $\frac{11}{12}=\frac{2}{3}y$ $y=\frac{11}{8}$ Solve Equations That Require Simplification In the following exercises, solve each equation requiring simplification. $5r-3r+9r=35-2$ $24x+8x-11x=-7-14$ $x=-1$ $\frac{11}{12}n-\frac{5}{6}n=9-5$ $-9\left(d-2\right)-15=-24$ $d=3$ Translate to an Equation and Solve In the following exercises, translate to an equation and then solve. 143 is the product of $-11$ and y . The quotient of b and and 9 is $-27$ . $\frac{b}{9}=-27;b=-243$ The sum of q and one-fourth is one. The difference of s and one-twelfth is one fourth. $s-\frac{1}{12}=\frac{1}{4};s=\frac{1}{3}$ Translate and Solve Applications In the following exercises, translate into an equation and solve. Ray paid$21 for 12 tickets at the county fair. What was the price of each ticket?

Janet gets paid $24 per hour. She heard that this is $\frac{3}{4}$ of what Adam is paid. How much is Adam paid per hour?$32

## Section 2.3 Solve Equations with Variables and Constants on Both Sides

Solve an Equation with Constants on Both Sides

Larry and Tom were standing next to each other in the backyard when Tom challenged Larry to guess how tall he was. Larry knew his own height is 6.5 feet and when they measured their shadows, Larry’s shadow was 8 feet and Tom’s was 7.75 feet long. What is Tom’s height?
6.25
Ciid
6.25
Big
Wayne is hanging a string of lights 57 feet long around the three sides of his patio, which is adjacent to his house. the length of his patio, the side along the house, is 5 feet longer than twice it's width. Find the length and width of the patio.
Ciid
tyler
tyler
tyler
tyler
SOH = Sine is Opposite over Hypotenuse. CAH= Cosine is Adjacent over Hypotenuse. TOA = Tangent is Opposite over Adjacent.
tyler
H=57 and O=285 figure out what the adjacent?
tyler
Amara currently sells televisions for company A at a salary of $17,000 plus a$100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a$20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
what is the quantity and price of the televisions for both options?
karl
Amara has to sell 120 televisions to make 29,000 of the salary of company B. 120 * TV 100= commission 12,000+ 17,000 = of company a salary 29,000 17000+
Ciid
Amara has to sell 120 televisions to make 29,000 of the salary of company B. 120 * TV 100= commission 12,000+ 17,000 = of company a salary 29,000
Ciid
I'm mathematics teacher from highly recognized university.
here a question professor How many soldiers are there in a group of 27 sailors and soldiers if there are four fifths as many sailors as soldiers? can you write out the college you went to with the name of the school you teach at and let me know the answer I've got it to be honest with you
tyler
is anyone else having issues with the links not doing anything?
Yes
Val
chapter 1 foundations 1.2 exercises variables and algebraic symbols
June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as the smaller cooler. How many gallons can each cooler hold? Enter the answers in decimal form.
Joseph would like to make 12 pounds of a coffee blend at a cost of $6.25 per pound. He blends Ground Chicory at$4.40 a pound with Jamaican Blue Mountain at $8.84 per pound. How much of each type of coffee should he use? Samer 4x6.25=$25 coffee blend 4×4.40= $17.60 ground chicory 4x8.84= 35.36 blue mountain. In total they will spend for 12 pounds$77.96 they will spend in total
tyler
DaMarcus and Fabian live 23 miles apart and play soccer at a park between their homes. DaMarcus rode his bike for three-quarters of an hour and Fabian rode his bike for half an hour to get to the park. Fabian’s speed was six miles per hour faster than DaMarcus’ speed. Find the speed of both soccer players.
i need help how to do this is confusing
what kind of math is it?
Danteii
help me to understand
huh, what is the algebra problem
Daniel
How many soldiers are there in a group of 27 sailors and soldiers if there are four fifths many sailors as soldiers?
tyler
What is the domain and range of heaviside
What is the domain and range of Heaviside and signum
Christopher
25-35
Fazal
The hypotenuse of a right triangle is 10cm long. One of the triangle’s legs is three times the length of the other leg. Find the lengths of the three sides of the triangle.
Tickets for a show are $70 for adults and$50 for children. For one evening performance, a total of 300 tickets were sold and the receipts totaled \$17,200. How many adult tickets and how many child tickets were sold?
A 50% antifreeze solution is to be mixed with a 90% antifreeze solution to get 200 liters of a 80% solution. How many liters of the 50% solution and how many liters of the 90% solution will be used?
June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as the smaller cooler. How many gallons can each cooler hold?