Question 150515
{{{abs(x-7)<=2}}} Start with the given inequality



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


{{{x-7 >= -2}}} and {{{x-7 <= 2}}} Break up the absolute value inequality using the given rule



{{{-2 <= x-7 <= 2}}} Combine the two inequalities to get a compound inequality




{{{5 <= x <= 9}}} Add 7 to  all sides



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Answer:


So our answer is


{{{5 <= x <= 9}}}




So the answer in interval notation is   <font size="8">[</font>*[Tex \LARGE \bf{5,9}]<font size="8">]</font>



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|5 \le x \le 9\right\}]



Here's the graph of the solution set


{{{drawing(500,80,0, 14,-10, 10,
number_line( 500, 0, 14 ,5,9),

blue(line(5,0,9,0)),
blue(line(5,0.30,9,0.30)),
blue(line(5,0.15,9,0.15)),
blue(line(5,-0.15,9,-0.15)),
blue(line(5,-0.30,9,-0.30))

)}}} Graph of the solution set


Note:

There is a <b>closed</b> circle at {{{x=5}}} which means that we're including this value in the solution set

Also, there is a <b>closed</b> circle at {{{x=9}}} which means that we're including this value in the solution set.