Questions on Algebra: Absolute value answered by real tutors!

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Question 151066: please solve and show work
-3|x+4|=-6x
: please solve and show work
-3|x+4|=-6x

Answer by vleith(1156) About Me  (Show Source):
You can put this solution on YOUR website!
Given-3abs(x+4)=-6x
abs(x+4)=2x
So
x+4 = 2x
4 = x
AND
-(x+4) = 2x
x+4 = -2x
4 = -3x
-4/3 = x
Question 151066: please solve and show work
-3|x+4|=-6x
: please solve and show work
-3|x+4|=-6x

Answer by jim_thompson5910(9162) About Me  (Show Source):
You can put this solution on YOUR website!
-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 not true, this means that x=-4/3 is not a solution.


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Answer:

So the only solution is x=4