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

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Question 151066: please solve and show work
-3|x+4|=-6x
Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given-3abs%28x%2B4%29=-6x+
abs%28x%2B4%29=2x+
So
x+4 = 2x
4 = x
AND
-(x+4) = 2x
x+4 = -2x
4 = -3x
-4/3 = x

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
-3%2Aabs%28x%2B4%29=-6x Start with the given equation.


abs%28x%2B4%29=2x Divide both sides by -3.


Remember, the equation abs%28x%29=a breaks down to x=a or x=-a. So in this case, abs%28x%2B4%29=2x breaks down to


x%2B4=2x or x%2B4=-2x


Let's solve the first equation x%2B4=2x


x%2B4=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=%28-4%29%2F%28-1%29 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%2Aabs%28x%2B4%29=-6x Start with the given equation.


-3%2Aabs%284%2B4%29=-6%284%29 Plug in x=4


-3%2Aabs%284%2B4%29=-24 Multiply


-3%2Aabs%288%29=-24 Add


-3%2A%288%29=-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%2B4=-2x


x%2B4=-2x Start with the second equation.


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


x%2B2x=-4 Add 2x to both sides.


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


x=-%284%29%2F%283%29 Divide both sides by 3 to isolate x.


So the second possible solution is x=-%284%29%2F%283%29





However, we must check it

Check:
-3%2Aabs%28x%2B4%29=-6x Start with the given equation.


-3%2Aabs%28-4%2F3%2B4%29=-6%28-4%2F3%29 Plug in x=-4%2F3


-3%2Aabs%28-4%2F3%2B4%29=8 Multiply


-3%2Aabs%28-8%2F3%29=8 Add


-3%2A%288%2F3%29=8 Take the absolute value


-8=8 Multiply


Since the equation is not true, this means that x=-4%2F3 is not a solution.


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Answer:

So the only solution is x=4