Question 151066
{{{-3*abs(x+4)=-6x}}} Start with the given equation.



{{{abs(x+4)=2x}}} Divide both sides by -3.



Remember, the equation {{{abs(x)=a}}} breaks down to {{{x=a}}} or {{{x=-a}}}. So in this case, {{{abs(x+4)=2x}}} breaks down to



{{{x+4=2x}}} or {{{x+4=-2x}}}



Let's solve the first equation {{{x+4=2x}}}



{{{x+4=2x}}} Start with the first equation.



{{{x=2x-4}}} Subtract {{{4}}} from both sides.



{{{x-2x=-4}}} Subtract {{{2x}}} from both sides.



{{{-x=-4}}} Combine like terms on the left side.



{{{x=(-4)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{x}}}.



{{{x=4}}} Reduce.



So the first possible solution is {{{x=4}}} 



However, we must check it


Check:

{{{-3*abs(x+4)=-6x}}} Start with the given equation.



{{{-3*abs(4+4)=-6(4)}}} Plug in {{{x=4}}} 



{{{-3*abs(4+4)=-24}}} Multiply



{{{-3*abs(8)=-24}}} Add



{{{-3*(8)=-24}}} Take the absolute value



{{{-24=-24}}} Multiply



Since the equation is true, this means that {{{x=4}}} is a solution.



So the first solution is {{{x=4}}}


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Now let's solve the second equation {{{x+4=-2x}}}



{{{x+4=-2x}}} Start with the second equation.



{{{x=-2x-4}}} Subtract {{{4}}} from both sides.



{{{x+2x=-4}}} Add {{{2x}}} to both sides.



{{{3x=-4}}} Combine like terms on the left side.



{{{x=-(4)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



So the second possible solution is {{{x=-(4)/(3)}}} 






However, we must check it


Check:

{{{-3*abs(x+4)=-6x}}} Start with the given equation.



{{{-3*abs(-4/3+4)=-6(-4/3)}}} Plug in {{{x=-4/3}}} 



{{{-3*abs(-4/3+4)=8}}} Multiply



{{{-3*abs(-8/3)=8}}} Add



{{{-3*(8/3)=8}}} Take the absolute value



{{{-8=8}}} Multiply



Since the equation is <font size=4><b>not</b></font> true, this means that {{{x=-4/3}}} is <font size=4><b>not</b></font> a solution.



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Answer:


So the only solution is {{{x=4}}}