Absolute Value Equations and Inequalities

One-Step Absolute Value Equations

100

l3xl=27

x=-9,9

200

 lx+5l=10

x=-15, 5

300

l4x+22l=30

x=-13, 8

400

|8/3p|=4

p=-3/2,3/2

500

|2/3p -3| =7

{15, -6}

Multi-Step Absolute Value Equations

100

lv+8l-5=2

v=-15,-1

200

l5xl+5=45

x=-8,8

300

6|5x -1| -9 =57

6l1-5xl-9=57

x=-2, 12/5

400

|8x + 4|/2=18

{4, -5}

500

2|10x + 4| + 6 = 22

x = {2/5, -6/5}

Word Problems

100

Write the inequality

A number m is not more than 22

m<= 22

200

The temperature in Ely MN has never been below -50

e >=-50

300

Elaina's goal was to shoot 10 three pointers every game. She would be happy if she shot within 2 of that goal. Write and solve an absolute equation to find her maximum and minimum shots. 

|x - 10| = 2

x = {8, 12}

400

Porter runs every week. The maximum distance he runs is 15 miles. The minimum distance is 5 miles. Write an absolute equation that would have the max and min for the solutions.

|x - 10| = 5

500

Amy is selling her electric scooter. She won't take any lower than $180 and figures the most she will get is $500. Write an absolute equation that would have these numbers as the minimum and maximum prices. 

|x -340| = 160

One and two Step Inequalities

100

Solve and graph

6n<18

n< 3

200

Solve and Graph

x - 2 < 8

x<10

300

Solve and graph

1+b<4

b<3

400

Solve and Graph

10p-4<36

p<4

500

5 + 1/5b<10

b<25

Multi-Step Inequalities

100

Solve and graph

x+2+2<4

x < 0

200

Solve and graph

2x+3>7

x > 2

300

Solve and graph

2x + 2 - 1< -11

x < -5

400

Solve and graph

5x+9+3>7

x > -1

500

9 + 1/7x > 21

x > 84