Question 180808

{{{abs(2x-6)-2<2}}} Start with the given inequality

{{{abs(2x-6)<4}}} Add 2 to both sides.

Break up the absolute value (remember, if you have {{{abs(x)< a}}}, then {{{x > -a}}} and {{{x < a}}})

{{{2x-6 > -4}}} and {{{2x-6 < 4}}} Break up the absolute value inequality using the given rule

{{{-4 < 2x-6 < 4}}} Combine the two inequalities to get a compound inequality

{{{2 < 2x < 10}}} Add 6 to  all sides

{{{1 < x < 5}}}  Divide all sides by 2 to isolate x

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Answer:

So our answer is

{{{1 < x < 5}}}

which looks like this in interval notation

*[Tex \LARGE \left(1,5\right)]

Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|1 < x < 5\right\}]