|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)

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

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|