Equations - Variables on Both Sides / Absolute Value Equations

Absolute value is defined as...

• always positive numbers
• negative numbers becoming positive
• distance from zero
• numbers on the number line

What is always your last step of solving equations with absolute values?

• Your last step depends on the equation.

• Solve for the unknown answer.

• Check your answer.

• Celebrate that you finished the problem!

∣ 2x + 9 ∣ = 15

• x = 3

• x = 3, -6

• x = 3, -12

• x = 6, -12

Solve |x – 12| - 3 = 11.

• x = -2, -26

• x = -2, 26

• x = 3, 25

• x = 4, -7

|−2n| + 10 = −50

• r = 30, -30

• r = 20,-20

• r = -5,5

• No Solution

Solve for r.

−2|−2r − 4| = -12

• r = 5,1

• r = -5,-1

• r = -5,1

• No Solution

|3m - 9| = 18

• m = 9,-3

• m = 9,3

• m = 9

• no solution

2|a - 5| = 22

• a = 16

• a = 16, -6

• a = 16, 6

• no solution