Question

Solve the fallowing absolute value inequality
3 |x-7| ≤ 27

Answer 1

x ≤ 16 and x ≥ -2

Explanation:

3 |x-7| ≤ 27

• divide both sides by 3:

|x-7| ≤ 9

• first assume the positive case of the absolute value:

x-7 ≤ 9

• add 7 to both sides:

x ≤ 16

• Now, go back to the absolute value and assume the negative case.

-(x-7) ≤ 9

-x+7 ≤ 9

• subtract 7 from both sides:

-x ≤ 2

• divide each side by -1 and flip the inequality sign:

x ≥ -2