# Solve for z 1/(6z)+1 1/6=-48

16z+116=-48
Convert 116 to an improper fraction.
A mixed number is an addition of its whole and fractional parts.
16z+1+16=-48
Add 1 and 16.
Write 1 as a fraction with a common denominator.
16z+66+16=-48
Combine the numerators over the common denominator.
16z+6+16=-48
Add 6 and 1.
16z+76=-48
16z+76=-48
16z+76=-48
Move all terms not containing z to the right side of the equation.
Subtract 76 from both sides of the equation.
16z=-48-76
To write -48 as a fraction with a common denominator, multiply by 66.
16z=-48⋅66-76
Combine -48 and 66.
16z=-48⋅66-76
Combine the numerators over the common denominator.
16z=-48⋅6-76
Simplify the numerator.
Multiply -48 by 6.
16z=-288-76
Subtract 7 from -288.
16z=-2956
16z=-2956
Move the negative in front of the fraction.
16z=-2956
16z=-2956
Set up the rational expression with the same denominator over the entire equation.
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 6z. The -2956 expression needs to be multiplied by zz to make the denominator 6z.
16z=-2956⋅zz
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 6z.
295(z)
Multiply 295 by z.
16z=-295z6z
16z=-295z6z
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
1=-(295z)
Rewrite the equation as -(295z)=1.
-(295z)=1
Multiply 295 by -1.
-295z=1
Divide each term by -295 and simplify.
Divide each term in -295z=1 by -295.
-295z-295=1-295
Cancel the common factor of -295.
Cancel the common factor.
-295z-295=1-295
Divide z by 1.
z=1-295
z=1-295
Move the negative in front of the fraction.
z=-1295
z=-1295
The result can be shown in multiple forms.
Exact Form:
z=-1295
Decimal Form:
z=-0.00338983…
Solve for z 1/(6z)+1 1/6=-48

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