Question 714840
{{{abs(3x-7)<=13}}}
 
If {{{3x-7>=0}}} --> {{{abs(3x-7)=3x-7}}} and the inequality is {{{3x-7<=13}}}
 
If {{{3x-7<0}}} --> {{{abs(3x-7)=-(3x-7)}}} and the inequality is {{{-(3x-7)<=13}}}
Multiplying both sides tiles (-1) and reversing the "less than" sign, we get an equivalent inequality
{{{-(3x-7)<=13}}} --> {{{3x-7>=-13}}} <--> {{{-12<=3x-7}}}
 
Both cases can be written together as {{{-12<=3x-7<=13}}}
Adding 7 to all three sides of the compound inequality yields an equivalent inequality.
{{{-12<=3x-7<=13}}} --> {{{-12+7<=3x-7+7<=13+7}}} --> {{{-6<=3x<=20}}}
Dividing by 3 all three sides of the compound inequality yields an equivalent inequality that is the solution.
{{{-6<=3x<=20}}} --> {{{-6/3<=3x/3<=20/3}}} --> {{{highlight(-2<=x<=20/3)}}}