Absolute Value Equations & Inequalities

Solve this equation. 
|-6x| = 30

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

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Solve the equation. 
4|n + 8| = 56

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

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

8 + |4v - 7| ≥ 17

• No solution

• v ≥ 9

• v ≥ 4

• $v\le-\frac{1}{2}$ or $v\ge4$

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve the inequality. 
|k| - 6 ≤ -1

• k ≤ 5
• k ≤ -5
• k ≤ -5, 5
• -5 ≤ k ≤ 5

Tags

CCSS.HSA.REI.B.3

Solve the equation.

 $4+\left|-3+a\right|=0$  

• 6, -6

• 5

• 5, -5

• No Solution

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

Solve the inequality

 $4\left|-8+x\right|<72$  

• -10, 26

• -10 < x < 26

• 10 < x < 26

• x < -10 or x > 26

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve the inequality.

 $\left|4r\right|>12$  

• r < -3 or r > 3

• -3 < r < 3

• -3, 3

• r > 3

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve the inequality.

 $\left|n-7\right|<3$  

• -10 < n < 10

• n < 4 or n > 10

• 4, 10

• 4 < n < 10

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

• cannot be
• is always
• can be

Answer explanation

The order of operations for this problem is:

calculate a-b

calculate c-d

subtract the latter from the former

apply the absolute value

Since the last step is applying the absolute value, the answer will always be positive.