Question #481d4

1 Answer
Sep 26, 2017

Answer:

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#