Question

Question #481d4

Answer 1

There are not two answers; there are an infinite number of solutions within the interval `-6 <= x <= 4`

Explanation:

Given: `| x+1 | <= 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:

`-(x+1) <= 5` and `x+1 <= 5`

Multiply the first equation by -1:

`x+1 >= -5` and `x+1 <= 5`

Subtract 1 from both sides of both inequalities:

`x >= -6` and `x <= 4`

This can be written as:

`-6 <= x <=4`