Question

olve and graph the inequality.
StartAbsoluteValue x plus 7 EndAbsoluteValue greater than or equals 5
Question content area bottom
Part 1
Choose the correct answer below.
A.negative 12 less than or equals x less than or equals minus 2
negative 12 less than or equals x less than or equals minus 2
B.x less than or equals minus 5 or x greater than or equals 5
x less than or equals minus 5 or x greater than or equals 5
C.x greater than or equals minus 2
x greater than or equals minus 2
D.x less than or equals minus 12 or x greater than or equals minus 2
x less than or equals minus 12 or x greater than or equals minus 2

Answer 1

Solve |x + 7| ≥ 5.

This means x + 7 ≥ 5 or x + 7 ≤ −5.

- x + 7 ≥ 5 ⇒ x ≥ −2
- x + 7 ≤ −5 ⇒ x ≤ −12

So the solution is x ≤ −12 or x ≥ −2, i.e. (−∞, −12] ∪ [−2, ∞). This is answer D.

Graph: closed dot at −12 with a ray left, and closed dot at −2 with a ray right.