# Solve for y |y-4|=|8y+3| |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)
Solve y-4=8y+3 for y.
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
Solve y-4=-(8y+3) for y.
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|

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