Question 173314


{{{4*abs(3x)-5<=5}}} Start with the given inequality



{{{4*abs(3x)<=10}}} Add 5 to both sides.



{{{abs(3x)<=10/4}}} Divide both sides by 4



{{{abs(3x)<=5/2}}} Reduce




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


{{{3x >= -5/2}}} and {{{3x <= 5/2}}} Break up the absolute value inequality using the given rule



{{{-5/2 <= 3x <= 5/2}}} Combine the two inequalities to get a compound inequality



{{{-(5/2)/3 <= x <= (5/2)/3}}}  Divide all sides by 3 to isolate x



{{{-5/6 <= x <= 5/6}}}  Reduce




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Answer:


So our answer is


{{{-5/6 <= x <= 5/6}}}





So the answer in interval notation is   <font size="8">[</font>*[Tex \LARGE \bf{-\frac{5}{6},\frac{5}{6}}]<font size="8">]</font>



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|-\frac{5}{6} \le x \le \frac{5}{6}\right\}]