How do you solve #-9 <= -3x+15 <= 12#?

1 Answer
Roy Ø.
May 11, 2018

#-9<=-3x+15<=12# when #1<=x<=8#

Explanation:

Let us start with a graph of the inequality:
enter image source here

If we define #f(x)=-3x+15# we are interested in the value area for x that will give values of f(x) between -9 and 15, which is the shaded area on the graph.
Reading directly on the graph, we see that #1<=x<=8# fulfills the inequality.

Mathematically we would solve it by treating the two inequalities separately:
#-9<=f(x)=-3x+15#
Add #3x+9# on both sides:
#3x<=15+9=24#
#x<=8# This is the upper limit of the area.

The lower:
#f(x)=-3x+15<=12#
Add 3x-12 on both sides to move 3x to one side and the constants to the other:
#15-12=3<=3x#
This gives #x>=1#

The values for x fulfilling the inequality is, therefore
#1<=x<=8#

Which is what we could read directly from the graph.

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