How do you solve #3x+2<=5(x-4)#?

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Answer 1 · 2016-12-10T20:41:17

#x >= 22#

First, expand the terms within parenthesis:

#3x + 2 <= 5x - 20#

Now, isolate the #x# terms on one side of the inequality and the constants on the other while keeping the inequality balanced:

#3x - 3x + 2 + 20 <= 5x - 3x - 20 + 20#

#0 + 2 + 20 >= 5x - 3x - 0#

#22 <= 2x#

#22/2 <= (2x)/2#

#11 <= x#

Now to state in terms of #x# we need to reverse or "flip" the inequality:

#x >= 22#