Absolute Value Inequalities

Solve the absolute Value inequality and graph. 

• A

• B

• C

• D

What is the correct first step?

• divide by 10

• multiply by 10

• make it two inequalities with an "or"

• make it two inequalities with and "and"

| x - 2 | > 3
Is this an "and"  or an "or" problem?

• and

• or

What is the first step?

• Get the absolute value alone by dividing both sides by 5

• Drop the absolute value bars and add 7 and 5 together

• Get the absolute value alone by subtracting 5 from both sides

Solve:
3 | 2x + 7| + 7 < 4

• x < -3 and x > -5/3

• x < -3 and x > -4

• all real numbers

• no solution

Solve:
|x + 4| + 8 > 2

• x < -3 and x > -5/3

• x < -3 and x > -4

• all real numbers

• no solution

Solve.
-5|x - 4| > 20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

Solve. 
|2x - 12| + 8  = 8 

• x = 6 or x = -2

• x = 6 or x = -6

• no solution

• x = 6

Solve.
-5|x - 4| < 20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

| x + 3 | ≤ 2

• No Solution

• All Real Numbers

• -5 ≤ x ≤ -1

• 1 ≤ x ≤ 5