Question 830963
8-|x+2|=5 and 8(-1)|x+2|=5  are not the same equation; they are not equivalent.  That could be what is confusing you.  The second of those two would be -8*|x+2|=5.


If you are given the first equation:
{{{8-abs(x+2)=5}}}
{{{-abs(x+2)=5-8}}}
{{{-abs(x+2)=-3}}}
{{{abs(x+2)=3}}}
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Consider the conditions of x+2 being positive or zero; and of being negative.
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{{{x+2>=0}}}, then {{{abs(x+2)=x+2=3}}}
{{{x=3-2}}}
{{{highlight(x=1)}}}
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{{{x+2<0}}}, then {{{abs(x+2)=-x-2=3}}}
{{{x+2=-3}}}
{{{x=-3-2}}}
{{{highlight(x=-5)}}}
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You SHOULD check each of these solutions for x in the original (given) equation to see if either of them fails as a solution.  x=-5 will work.  Actually, x=1 will also work.



Note that in most absolute value EQUATIONS, you can treat the absolute value as a variable until it is isolated to be analyzed more closely.