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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