How do you solve #10 < 3x+4<12#?

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Answer 1 · 2017-01-07T15:53:29

See full solution process below in the explanation

To solve this inequality set we must perform the same operations to each of the three terms to find #x# while keeping the inequalities balanced.

First, we will subtract #color(red)(4)# from each term:

#10 - color(red)(4) < 3x + 4 - color(red)(4) < 12 - color(red)(4)#

#6 < 3x + 0 < 8#

#6 < 3x < 8#

Now. we can divide each term by #color(red)(3)# to solve for #x# while keeping the entire inequality set balanced.

#6/color(red)(3) < (3x)/color(red)(3) < 8/color(red)(3)#

#2 < (color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) < 8/3#

#2 < x < 8/3#