Absolute Value Equation and Inequality Practice

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

• and

• or

Solve the absolute Value inequality and graph. 

• A

• B

• C

• D

What is the correct first step?

• divide both sides by 10

• multiply both sides by 10

• make it two inequalities with an "or"

• make it two inequalities with and "and" or a between statement

• no solution
• a> -1/6 or a< -5/6
• a>1/2 or a< -3/2
• all real numbers

• no solution
• x > 2 or x < -22
• -22 < x < 2
• all real numbers

2t - 3 | - 5 > 16

• No Solution

• All Real Numbers

• t < -2  or  t > 5

• -2 < t < 5

An absolute value inequality is

• an inequality that contains an absolute value expression

• impossible to solve

• an equation that contains an absolute value expression

• always going to have two solutions

What is ALWAYS the first GOAL in solving an absolute value inequality?

• set up the positive case

• set up the negative case

• isolate the absolute value expression

• multiply or divide by the coefficient of the variable

| x + 3 | ≤ 2

• No Solution

• x ≤ -1

• -5 ≤ x and x ≤ -1

• 1 ≤ x and x ≤ 5 ... 1 ≤ x ≤ 5

| x + 3 | > 8

• No Solution

• All Real Numbers

• x < -11  or  x > 5

• -5 < x < 11