How do you solve #-2<=2x-4<4#?

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Answer 1 · 2017-05-03T12:30:56

See the entire solution process below:

First, add #color(red)(4)# to each of the segments in the system of inequalities to isolate the #x# term while keeping the system balanced:

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

#2 <= 2x - 0 < 8#

#2 <= 2x < 8#

Now, divide each segment by #color(red)(2)# to solve for #x# while keeping the system balanced:

#2/color(red)(2) <= (2x)/color(red)(2) < 8/color(red)(2)#

#1 <= (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 4#

#1 <= x < 4#

Or

#x >= 1# and #x < 4#

Or, in interval notation:

#[1, 4)#