|3-5a4|-13=23

Add 13 to both sides of the equation.

|3-5a4|=23+13

Combine the numerators over the common denominator.

|3-5a4|=2+13

Add 2 and 1.

|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

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

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