Question 201217
{{{abs(x)<=14}}} Start with the given inequality



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


{{{x >= -14}}} and {{{x <= 14}}} Break up the absolute value inequality using the given rule



{{{-14 <= x <= 14}}} Combine the two inequalities to get a compound inequality




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Answer:


So our answer is


{{{-14 <= x <= 14}}}



So the answer in interval notation is   <font size="8">[</font>*[Tex \LARGE \bf{-14,14}]<font size="8">]</font>



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|-14 \le x \le 14\right\}]



Here's the graph of the solution set on a number line:


{{{drawing(500,80,-19, 19,-10, 10,
number_line( 500, -19, 19 ,-14,14),

blue(line(-14,0,14,0)),
blue(line(-14,0.30,14,0.30)),
blue(line(-14,0.15,14,0.15)),
blue(line(-14,-0.15,14,-0.15)),
blue(line(-14,-0.30,14,-0.30))

)}}} Graph of the solution set


Note:

There is a <b>closed</b> circle at {{{x=-14}}} which means that we're including this value in the solution set

Also, there is a <b>closed</b> circle at {{{x=14}}} which means that we're including this value in the solution set.