2.6 Abs. Val. Inequalities

Solve the absolute Value inequality and graph. 

• A
• B
• C
• D

Which graph represents the solution to the absolute-value inequality:

I 3x + 9 I > 27

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Answer explanation

Remember what sort of graph > means for absolute-value.

|v + 8| − 5 = 2 

• {-1,-15}
• {-1,-5}
• {-15,15}
• No Solution

| 3c - 5 | < -2

• No Solution
• All Real Numbers
• 1 < c < ⁷/₃
• c < 1  or  c > ⁷/₃

| n + 2 | - 3 ≥ -6

• No Solution
• All Real Numbers
• n ≤ -5  or  n ≥ 1
• -5 ≤ n ≤ 1

Solve.

3|2d + 9| + 13 > 10

• d > 5 or d < -1

• d < -4 or d > 5

• No Solution

• All real numbers

Solve.
6 - 2|m -3| > -4

• -8 < m < 2
• m < -8 or m > 2
• m < -2 or m > 8
• -2 < m < 8

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

• no solution
• x > 2 or x < -22
• -22 < x < 2
• all real numbers

• no solution
• -6 < x < 26
• x < -6 or x > 26
• all real numbers