# Solve for a |(3-5a)/4|-1/3=2/3

|3-5a4|-13=23
Move all terms not containing |3-5a4| to the right side of the equation.
Add 13 to both sides of the equation.
|3-5a4|=23+13
Combine the numerators over the common denominator.
|3-5a4|=2+13
|3-5a4|=33
Divide 3 by 3.
|3-5a4|=1
|3-5a4|=1
Remove the absolute value term. This creates a ± on the right side of the equation because |x|=±x.
3-5a4=±1
Set up the positive portion of the ± solution.
3-5a4=1
Solve the first equation for a.
Multiply both sides of the equation by 4.
3-5a=1⋅(4)
Remove parentheses.
3-5a=1⋅(4)
Multiply 4 by 1.
3-5a=4
Move all terms not containing a to the right side of the equation.
Subtract 3 from both sides of the equation.
-5a=4-3
Subtract 3 from 4.
-5a=1
-5a=1
Divide each term by -5 and simplify.
Divide each term in -5a=1 by -5.
-5a-5=1-5
Cancel the common factor of -5.
Cancel the common factor.
-5a-5=1-5
Divide a by 1.
a=1-5
a=1-5
Move the negative in front of the fraction.
a=-15
a=-15
a=-15
Set up the negative portion of the ± solution.
3-5a4=-1
Solve the second equation for a.
Multiply both sides of the equation by 4.
3-5a=-1⋅4
Remove parentheses.
3-5a=-1⋅4
Multiply -1 by 4.
3-5a=-4
Move all terms not containing a to the right side of the equation.
Subtract 3 from both sides of the equation.
-5a=-4-3
Subtract 3 from -4.
-5a=-7
-5a=-7
Divide each term by -5 and simplify.
Divide each term in -5a=-7 by -5.
-5a-5=-7-5
Cancel the common factor of -5.
Cancel the common factor.
-5a-5=-7-5
Divide a by 1.
a=-7-5
a=-7-5
Dividing two negative values results in a positive value.
a=75
a=75
a=75
The solution to the equation includes both the positive and negative portions of the solution.
a=-15,75
The result can be shown in multiple forms.
Exact Form:
a=-15,75
Decimal Form:
a=-0.2,1.4
Mixed Number Form:
a=-15,125
Solve for a |(3-5a)/4|-1/3=2/3

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