Solving Inequalities with Absolute Value

The average temperature in Las Vegas in July is 110 degrees.  If the temperature can vary up to 10 degrees, which equation represents this situation?

• | x - 10 | < 110

• | 110 - x | < 10

• | x - 110 | < 10

• | 10 - x | < 110

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

| x + 3 | ≤ 2

• No Solution

• All Real Numbers

• -5 ≤ x ≤ -1

• 1 ≤ x ≤ 5

• no solution
• -6 ≤ r ≥ 8
• 6 > r > -8
• -6 < r < 8

• all real numbers
• no solution
• 0 < v < 6⁄7
• 0 ≤ v ≤ 6/7

no solution

-6 < x < 26

x < -6 or x > 26

all real numbers

• no solution

• -6 < x < 26

• x < -6 or x > 26

• all real numbers

• no solution
• all real numbers 
• -2 ≤ n ≤ 16
• n ≤ -2 or n ≥ 16

| 3c - 5 | < -2

• No Solution

• All Real Numbers

• 1 < c < ⁷/₃

• c < 1  or  c > ⁷/₃

| x + 1 | ≥ 3

• No Solution

• All Real Numbers

• x ≤ -4  or  x ≥ 2

• -4 ≤ x ≤ 2

| 12 + w | ≥ -5

• No Solution

• All Real Numbers

• w ≤ -17  or  w ≥ -7

• -17 ≤ w ≤ -7