# 2.7 Solve linear inequalities  (Page 7/8)

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## 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

Aziza is solving this equation-2(1+x)=4x+10
No. 3^32 -1 has exactly two divisors greater than 75 and less than 85 what is their product?
x^2+7x-19=0 has Two solutions A and B give your answer to 3 decimal places
3. When Jenna spent 10 minutes on the elliptical trainer and then did circuit training for20 minutes, her fitness app says she burned 278 calories. When she spent 20 minutes onthe elliptical trainer and 30 minutes circuit training she burned 473 calories. How manycalories does she burn for each minute on the elliptical trainer? How many calories doesshe burn for each minute of circuit training?
.473
Angelita
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Angelita
John left his house in Irvine at 8:35 am to drive to a meeting in Los Angeles, 45 miles away. He arrived at the meeting at 9:50. At 3:30 pm, he left the meeting and drove home. He arrived home at 5:18.
p-2/3=5/6 how do I solve it with explanation pls
P=3/2
Vanarith
1/2p2-2/3p=5p/6
James
Cindy
4.5
Ruth
is y=7/5 a solution of 5y+3=10y-4
yes
James
Cindy
Lucinda has a pocketful of dimes and quarters with a value of $6.20. The number of dimes is 18 more than 3 times the number of quarters. How many dimes and how many quarters does Lucinda have? Rhonda Reply Find an equation for the line that passes through the point P ( 0 , − 4 ) and has a slope 8/9 . Gabriel Reply is that a negative 4 or positive 4? Felix y = mx + b Felix if negative -4, then -4=8/9(0) + b Felix -4=b Felix if positive 4, then 4=b Felix then plug in y=8/9x - 4 or y=8/9x+4 Felix Macario is making 12 pounds of nut mixture with macadamia nuts and almonds. macadamia nuts cost$9 per pound and almonds cost $5.25 per pound. how many pounds of macadamia nuts and how many pounds of almonds should macario use for the mixture to cost$6.50 per pound to make?
Nga and Lauren bought a chest at a flea market for $50. They re-finished it and then added a 350 % mark - up Makaila Reply$1750
Cindy
the sum of two Numbers is 19 and their difference is 15
2, 17
Jose
interesting
saw
4,2
Cindy
Felecia left her home to visit her daughter, driving 45mph. Her husband waited for the dog sitter to arrive and left home 20 minutes, or 13 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her?
hola saben como aser un valor de la expresión
NAILEA
integer greater than 2 and less than 12
2 < x < 12
Felix
I'm guessing you are doing inequalities...
Felix
Actually, translating words into algebraic expressions / equations...
Felix
hi
Darianna
hello
Mister
Eric here
Eric
6
Cindy