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

1 Answer
Alan P.
Nov 26, 2015

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

Explanation:

#2(x-3) < 4(x+1/2)#

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

Subtract #(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 < 2x#

Divide both sides by #2#
(you can always multiply or divide by any amount #>0# without effecting the validity or orientation of the inequality)
#-4 < x#

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

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