Question

Solve |x + 7| < 6

Answer 1

Answer:

A) –13 < x < –1

Step-by-step 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

Answer:

A) - 13 < x < - 1

Step-by-step 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.