Question

Solve |x + 7| < 6

A)

–13 < x < –1

B)

–1 < x < –13

C)

–13 < x and x > –1

D)

–13 < x or x < –1

Answer 1

A) –13 < x < –1

Explanation:

|x + 7| < 6

Separate into possible cases

`x + 7 < 6 \\x +7 \geq 0`

Solve the inequalities

`x < - 1, x \geq -7\\x > -13, x < -7`

Find the intersections

`x = (-7, -1)\\x = (-13, -7)`

Find the union

Answer: A) –13 < x < –1

Answer 2

A) - 13 < x < - 1

Explanation:

1) Rewrite the inequality without the absolute value.

`- 6 < x + 7 < 6`

2) Subtract 7 from the whole equation.

`- 6 - 7 < x < 6 - 7`

3) Simplify.

`- 13 < x < - 1`

Therefor, the answer is the first option.