Absolute Value Equations

Is it a Solution?

100

|2x+6|=x has x= -2 as a solution. 

False

200

x= - 17 is a solution to: 

|6x-4|=38-4x. 

True or False?

True 

300

x= 3 is a solution to |7x+5|=6x - 44

False

400

The equation |5x+3|=3x+5 has 

(a) x= 1 only as a solution

(b) x= -1 only as a solution

(c) both x= 1 and x= -1 as solutions

(d) neither x= 1 and x= -1 as solutions

(a) x= 1 only as a solution

500

|4x+3|=2x-29 has 

(a) x=3 only as a solution

(b) x= -12 only as a solution 

(c) both x=3 and x= -12 as solutions

(d) neither x=3 or x= -12 as solutions

(d) neither x=3 or x= -12 as solutions

Fundamentals

100

Fill in the blank: |8| by definition means to find the __________ between ______ and _____ 

distance/8/0

or 

distance/0/8

200

Create two equations based on the absolute value equation: 

|w|=d-6

w=d-6 AND w= -d + 6

300

Solve for p and solve for k: 

|-9|=p

|k|=15

p=9 

k=15 and k = -15

400

Solve for g and solve for h:

|g|= -16

|-100|=h

g: no solution

h=100

500

Solve for y and solve for b (your answer should be an equation for b): 

|400-200|=y

|w|=b+4

y=200

b=w-4 and b= -w - 4

1-3 step

100

Solve for g: 

|6+g|=13

g=7 and g= -19

200

|x-4|= -5

no solution

300

Solve for y: 

|2x-9|=15

x=12 and x= -3

400

|x/5 + 2 | =4

x=10 and x= -30 

500

Solve for k: 

|5+ k/2 + 7 | = 18

k=12 and k= -60

Check your Answers!

100

|8x-10|=7x+25 has solution(s): 

x=35 and x= -1

200

|3x+30|=9-4x has solution(s): 

x=-3 

(not x=39)

300

|4x+3|=5x-12 has solution(s): 

x=15 

(not x=1)

400

|3x-12|=x has solution(s):

x=6 and x=3

500

|4x+120|=6x has solution(s): 

x=60

(not x= -12)

Isolate it first!

100

5|x|+1=16

x=3 and x= -3

200

-9 |x| + 4 = -32

x= 4 and x= -4 

300

3|x|+8=2

no solution

400

|x+3| / 4 + 5 = 8

x= 9 and x= -15

500

7|x+2|/4+8=22

x=6 and x= -10