How do you solve #2\leq 2x - 6< 4#?

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Answer 1 · 2018-01-16T15:28:18

See a solution process below:

First, add #color(red)(6)# to each segment of the system of inequalities to isolate the #x# term while keeping the system balanced:

#2 + color(red)(6) <= 2x - 6 + color(red)(6) < 4 + color(red)(6)#

#8 <= 2x - 0 < 10#

#8 <= 2x < 10#

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

#8/color(red)(2) <= (2x)/color(red)(2) < 10/color(red)(2)#

#4 <= (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 5#

#4 <= x < 5#

Or

#x >= 4#; #x < 5#

Or, in interval notation:

#[4, 5)#