How do you solve #|- 3s | \leq 3#?

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Answer 1 · 2017-09-21T18:03:03

The absolute value function has the piecewise definition:

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

#:.#

One can separate an inequality of the form:

#|f(x)|<=C#

Into:

#f(x) <= C and -f(x) <= C#

In the case of the inequality #|- 3s | \leq 3#, #f(x)# is replaced by # -3s#, therefore, we separate the inequality into:

#-3s <= 3 and -(-3s) <= 3#

Multiply both sides of the second equation by -1:

#-3s <= 3 and -3s >= -3#

Divide both sides of both equations by -3:

#s >= -1 and s<= 1#

This can be written as:

#-1 <= s <= 1#