How do you solve the inequality #5x < 2x - 6#?

1 Answer
Alan P.
Nov 23, 2016

#color(green)(x < -2)#

Explanation:

Remember that given an inequality:
[1]#color(white)("XXX")# you can add or subtract the same amount to/from both sides, and
[2]#color(white)("XXX")# you can multiply or divide both sides by any positive amount
without changing the validity or direction of the inequality.

Given:
#color(white)("XXX")color(green)(5x < 2x-6)#

We can subtract #color(green)(2x)# from both sides to get:
#color(white)("XXX")color(green)(3x < -6)#

Then, if we divide both sides by #color(green)3#
#color(white)("XXX")color(green)(x < -2)#

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