How do you solve the inequality 2(x-3) <4(x+1/2)2(x3)<4(x+12)?

1 Answer
Nov 26, 2015

Simplify the the expression on each side; add and subtract to isolate xx; then reverse the inequality to get
color(white)("XXX")x > -4XXXx>4

Explanation:

2(x-3) < 4(x+1/2)2(x3)<4(x+12)

Expand the expression on each side:
2x-6 < 4x + 22x6<4x+2

Subtract (2x+2)(2x+2) from both sides
(you can always subtract the same amount from both sides of an inequality with out effecting the validity or orientation of the inequality)
-8 < 2x8<2x

Divide both sides by 22
(you can always multiply or divide by any amount >0>0 without effecting the validity or orientation of the inequality)
-4 < x4<x

Reversal of inequality (doesn't really change it but makes it look more standard)
x > -1x>1