Question 837355
The absolute value is a variable until it is isolated and can be more carefully analyzed.


{{{abs(2a+7)=(3a+12)/3}}}
{{{abs(2a+7)=a+4}}}
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Solve for two different cases.
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CASE: {{{2a+7>=0}}}.
{{{abs(2a+7)=2a+7=a+4}}}
{{{a+7=4}}}
{{{a=-3}}}
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CASE: {{{2a+7<0}}}.
{{{abs(2a+7)=-2a-7=a+4}}}
{{{-3a+7=4}}}
{{{-3a=-3}}}
{{{a=1}}}
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Summary of Solution Answers:  {{{highlight(a=-3)}}} or {{{highlight(a=1)}}}
and you might want to check each solution to be sure that it works.