How do you solve #3x - 8< 5x - 4\leq 7#?

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Answer 1 · 2017-09-30T18:19:59

Given: #3x-8 < 5x - 4 <= 7#

Break into two inequalities:

#3x-8 < 5x - 4# and #5x - 4 <= 7#

Add 4 to both sides of both inequalities:

#3x-4 < 5x# and #5x <= 11#

Subtract #3x# form both sides of the first inequality and divide both sides of the second by 5:

#-4 < 2x# and #x <= 11/5#

Divide both sides of the first inequality by 2:

#-2 < x# and #x <= 11/5#

This can be written as:

#-2 < x <= 11/5#

I confirmed this using WolframAlpha