How do you solve #-2\leq 3x + 4< 13#?

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Answer 1 · 2017-06-12T02:43:32

See a solution process below:

First, subtract #color(red)(4)# from each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:

#-2 - color(red)(4) <= 3x + 4 - color(red)(4) < 13 - color(red)(4)#

#-6 <= 3x + 0 < 9#

#-6 <= 3x < 9#

Now, divide each segment by #color(red)(3)# to solve for #x# while keeping the system balanced:

#-6/color(red)(3) <= (3x)/color(red)(3) < 9/color(red)(3)#

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

#-2 <= x < 3#

Or

#x >= -2# and #x < 3#

Or, in interval notation:

#[-2, 3)#