Solve for a |2a+6|=|3a-6|

Math
|2a+6|=|3a-6|
Rewrite the absolute value equation as four equations without absolute value bars.
2a+6=3a-6
2a+6=-(3a-6)
-(2a+6)=3a-6
-(2a+6)=-(3a-6)
After simplifying, there are only two unique equations to be solved.
2a+6=3a-6
2a+6=-(3a-6)
Solve 2a+6=3a-6 for a.
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Move all terms containing a to the left side of the equation.
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Subtract 3a from both sides of the equation.
2a+6-3a=-6
Subtract 3a from 2a.
-a+6=-6
-a+6=-6
Move all terms not containing a to the right side of the equation.
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Subtract 6 from both sides of the equation.
-a=-6-6
Subtract 6 from -6.
-a=-12
-a=-12
Multiply each term in -a=-12 by -1
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Multiply each term in -a=-12 by -1.
(-a)⋅-1=(-12)⋅-1
Multiply (-a)⋅-1.
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Multiply -1 by -1.
1a=(-12)⋅-1
Multiply a by 1.
a=(-12)⋅-1
a=(-12)⋅-1
Multiply -12 by -1.
a=12
a=12
a=12
Solve 2a+6=-(3a-6) for a.
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Simplify -(3a-6).
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Apply the distributive property.
2a+6=-(3a)–6
Multiply.
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Multiply 3 by -1.
2a+6=-3a–6
Multiply -1 by -6.
2a+6=-3a+6
2a+6=-3a+6
2a+6=-3a+6
Move all terms containing a to the left side of the equation.
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Add 3a to both sides of the equation.
2a+6+3a=6
Add 2a and 3a.
5a+6=6
5a+6=6
Move all terms not containing a to the right side of the equation.
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Subtract 6 from both sides of the equation.
5a=6-6
Subtract 6 from 6.
5a=0
5a=0
Divide each term by 5 and simplify.
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Divide each term in 5a=0 by 5.
5a5=05
Cancel the common factor of 5.
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Cancel the common factor.
5a5=05
Divide a by 1.
a=05
a=05
Divide 0 by 5.
a=0
a=0
a=0
List all of the solutions.
a=12,0
Solve for a |2a+6|=|3a-6|

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