|y-4|=|8y+3|

Rewrite the absolute value equation as four equations without absolute value bars.

y-4=8y+3

y-4=-(8y+3)

-(y-4)=8y+3

-(y-4)=-(8y+3)

After simplifying, there are only two unique equations to be solved.

y-4=8y+3

y-4=-(8y+3)

Move all terms containing y to the left side of the equation.

Subtract 8y from both sides of the equation.

y-4-8y=3

Subtract 8y from y.

-7y-4=3

-7y-4=3

Move all terms not containing y to the right side of the equation.

Add 4 to both sides of the equation.

-7y=3+4

Add 3 and 4.

-7y=7

-7y=7

Divide each term by -7 and simplify.

Divide each term in -7y=7 by -7.

-7y-7=7-7

Cancel the common factor of -7.

Cancel the common factor.

-7y-7=7-7

Divide y by 1.

y=7-7

y=7-7

Divide 7 by -7.

y=-1

y=-1

y=-1

Simplify -(8y+3).

Apply the distributive property.

y-4=-(8y)-1⋅3

Multiply.

Multiply 8 by -1.

y-4=-8y-1⋅3

Multiply -1 by 3.

y-4=-8y-3

y-4=-8y-3

y-4=-8y-3

Move all terms containing y to the left side of the equation.

Add 8y to both sides of the equation.

y-4+8y=-3

Add y and 8y.

9y-4=-3

9y-4=-3

Move all terms not containing y to the right side of the equation.

Add 4 to both sides of the equation.

9y=-3+4

Add -3 and 4.

9y=1

9y=1

Divide each term by 9 and simplify.

Divide each term in 9y=1 by 9.

9y9=19

Cancel the common factor of 9.

Cancel the common factor.

9y9=19

Divide y by 1.

y=19

y=19

y=19

y=19

List all of the solutions.

y=-1,19

The result can be shown in multiple forms.

Exact Form:

y=-1,19

Decimal Form:

y=-1,0.1‾

Solve for y |y-4|=|8y+3|