Absolute Value Equations & Inequalities

Solve this equation. 
|-6x| = 30

• x = -5
• No solution
• x = 5, -5
• x = 5 

Solve the equation. 
|m| + 2 = 11

• m = -9
• m = 9
• m = -13, 9
• m = 9, -9

Solve the equation. 
4|n + 8| = 56

• n = 6
• n = -22
• n = 6, -22
• No solution

Solve the inequality.

|m| + 5 < 9

• m < 4

• m < -4

• m<4 , m>-4

• m < 4 , m <-4

Solve the inequality. (hint: isolate the absolute value).

8 + |4v - 7| ≥ 17

• v<1/2 , v ≥ 4

• v > -1/2 , v < 4

• v<-1/2 , v ≥ -4

• v<-1/2 , v ≥ 4

| 2x + 12 | < 8

Which is the correct first step?

• 2x + 12 < 8 and 2x+12 > -8

• 2x + 12 < 8 or 2x+12 > -8

• 2x + 12 < 8 and 2x+12 < -8

• 2x + 12 < 8 or 2x+12 < -8

Solve.

8 - 9|10r - 9| = -73

• r = 9/5, r = 0

• r = 0, r = 5

• r = 9/5, r = 1

• r = -63/10, r= 0

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