# Question 481d4

Sep 26, 2017

There are not two answers; there are an infinite number of solutions within the interval $- 6 \le x \le 4$

#### Explanation:

Given: $| x + 1 | \le 5$

Because the piecewise definition of the absolute value function is:

|f(x)| = {(f(x); f(x) >= 0),(-f(x); f(x) < 0):}#

One can separate the given inequality into two inequalities:

$- \left(x + 1\right) \le 5$ and $x + 1 \le 5$

Multiply the first equation by -1:

$x + 1 \ge - 5$ and $x + 1 \le 5$

Subtract 1 from both sides of both inequalities:

$x \ge - 6$ and $x \le 4$

This can be written as:

$- 6 \le x \le 4$