# Solve for z 8=1/(z+6) 8=1z+6
Rewrite the equation as 1z+6=8.
1z+6=8
Solve for z.
Multiply each term by z+6 and simplify.
Multiply each term in 1z+6=8 by z+6.
1z+6⋅(z+6)=8⋅(z+6)
Cancel the common factor of z+6.
Cancel the common factor.
1z+6⋅(z+6)=8⋅(z+6)
Rewrite the expression.
1=8⋅(z+6)
1=8⋅(z+6)
Simplify 8⋅(z+6).
Apply the distributive property.
1=8z+8⋅6
Multiply 8 by 6.
1=8z+48
1=8z+48
1=8z+48
Rewrite the equation as 8z+48=1.
8z+48=1
Move all terms not containing z to the right side of the equation.
Subtract 48 from both sides of the equation.
8z=1-48
Subtract 48 from 1.
8z=-47
8z=-47
Divide each term by 8 and simplify.
Divide each term in 8z=-47 by 8.
8z8=-478
Cancel the common factor of 8.
Cancel the common factor.
8z8=-478
Divide z by 1.
z=-478
z=-478
Move the negative in front of the fraction.
z=-478
z=-478
z=-478
The result can be shown in multiple forms.
Exact Form:
z=-478
Decimal Form:
z=-5.875
Mixed Number Form:
z=-578
Solve for z 8=1/(z+6)

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