# Solve for z |5z-2|=|z+6| |5z-2|=|z+6|
Rewrite the absolute value equation as four equations without absolute value bars.
5z-2=z+6
5z-2=-(z+6)
-(5z-2)=z+6
-(5z-2)=-(z+6)
After simplifying, there are only two unique equations to be solved.
5z-2=z+6
5z-2=-(z+6)
Solve 5z-2=z+6 for z.
Move all terms containing z to the left side of the equation.
Subtract z from both sides of the equation.
5z-2-z=6
Subtract z from 5z.
4z-2=6
4z-2=6
Move all terms not containing z to the right side of the equation.
Add 2 to both sides of the equation.
4z=6+2
Add 6 and 2.
4z=8
4z=8
Divide each term by 4 and simplify.
Divide each term in 4z=8 by 4.
4z4=84
Cancel the common factor of 4.
Cancel the common factor.
4z4=84
Divide z by 1.
z=84
z=84
Divide 8 by 4.
z=2
z=2
z=2
Solve 5z-2=-(z+6) for z.
Simplify -(z+6).
Apply the distributive property.
5z-2=-z-1⋅6
Multiply -1 by 6.
5z-2=-z-6
5z-2=-z-6
Move all terms containing z to the left side of the equation.
Add z to both sides of the equation.
5z-2+z=-6
Add 5z and z.
6z-2=-6
6z-2=-6
Move all terms not containing z to the right side of the equation.
Add 2 to both sides of the equation.
6z=-6+2
Add -6 and 2.
6z=-4
6z=-4
Divide each term by 6 and simplify.
Divide each term in 6z=-4 by 6.
6z6=-46
Cancel the common factor of 6.
Cancel the common factor.
6z6=-46
Divide z by 1.
z=-46
z=-46
Simplify -46.
Cancel the common factor of -4 and 6.
Factor 2 out of -4.
z=2(-2)6
Cancel the common factors.
Factor 2 out of 6.
z=2⋅-22⋅3
Cancel the common factor.
z=2⋅-22⋅3
Rewrite the expression.
z=-23
z=-23
z=-23
Move the negative in front of the fraction.
z=-23
z=-23
z=-23
z=-23
List all of the solutions.
z=2,-23
The result can be shown in multiple forms.
Exact Form:
z=2,-23
Decimal Form:
z=2,-0.6‾
Solve for z |5z-2|=|z+6|

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