Abs Value Cheat Sheet

Absolute Value Cheat Sheet

With zero

With negative numbers

Example

Example

Example

Example

Example

With positive numbers

14''-18''

Scene 04

11''-14''

Example

Example

|2x - 3| + 5 < 18 - 5 - 5 |2x - 3| < 13 2x - 3 < 13 AND 2x - 3 > -13 + 3 + 3 +3 + 3 2x < 16 2x > -10 x < 8 x > -5

Step 1: Get the absolute value alone

Step 2: Drop the absolute value sign, rewrite the original inequality, and then write a second inequality where you change the sign to greater than and make the number negative

Step 3: Solve both inequalities

Step 4: Graph both inequalties

|x - 2| + 1 > 5 -1 -1 |x - 2| > 4 x - 2 > 4 OR x - 2 < -4 + 2 + 2 +2 + 2 x > 6 x < -2

Step 1: Get the absolute value alone

Step 2: Drop the absolute value sign, rewrite the original inequality, and then write a second inequality where you change the sign to less than and make the number negative

Step 3: Solve both inequalities (Already done)

Step 4: Graph both inequalties

|x - 2| + 3 < 3 -3 -3 |x - 2| < 0 No Solution

Step 1: Get the absolute value alone

Step 2: There are no real numbers that can be substituted for "x" to make the absolute value inequality less than zero.

Note - if the sign was ≤, then the absolute value could be solved when equal to zero. It just cannot be less than zero.

|x| + 12 < 1 -12 -12 |x| < -11 No Solution

Step 1: Get the absolute value alone

Step 2: No real numbers can be substituted for "x" to make the absolute value inequality less than -11.

Give it a try! Substitute any number in for "x" and see if you get a true statement.

4|x| +10 > 2 -10 -10 4|x| > -8 4 4 |x| > -2

Step 1: Get the absolute value alone

Step 2: All real numbers are greater than -2

2|x| + 5 > 5 -5 -5 2|x| > 0 2 2 |x| > 0

Step 1: Get the absolute value alone

Step 2: All real numbers are greater than 0

|x - 2| + 3 < 3 -3 -3 |x - 2| < 0 No Solution

Step 1: Get the absolute value alone

Step 2: There are no real numbers that can be substituted for "x" to make the absolute value inequality less than zero.

Note - if the sign was ≤, then the absolute value could be solved when equal to zero. It just cannot be less than zero.