How do you solve and graph #x - 2 ≤ 2/3(x) - 3#?

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Answer 1 · 2018-07-24T18:57:48

#x < -3#

#x - 2 <= 2/3x-3#

Subtract #color(blue)(2/3x)# from both sides:
#x - 2 quadcolor(blue)(-quad2/3x) <= 2/3x - 3 quadcolor(blue)(-quad2/3x)#

#1/3x - 2 <= -3#

Add #color(blue)2# to both sides:
#1/3x - 2 quadcolor(blue)(+quad2) <= -3 quadcolor(blue)(+quad2)#

#1/3x <= -1#

Multiply both sides by #color(blue)3#:
#1/3x color(blue)(*3) <= -1 color(blue)(*3)#

#x < -3#

Here's a graph of it on a number line:
enter image source here
(mathwarehouse.com)

The open circle on #-3# means that it is not a solution (but anything less than it is).

Hope this helps!