Solve for z -1/4z+7/8=-1/2

$- \frac{1}{4} z + \frac{7}{8} = - \frac{1}{2}$

Step 1

Combine $z$ and $\frac{1}{4}$ .

$- \frac{z}{4} + \frac{7}{8} = - \frac{1}{2}$

Step 2

Move all terms not containing $z$ to the right side of the equation.

Subtract $\frac{7}{8}$ from both sides of the equation.

$- \frac{z}{4} = - \frac{1}{2} - \frac{7}{8}$

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{z}{4} = - \frac{1}{2} \cdot \frac{4}{4} - \frac{7}{8}$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{4}{4}$ .

$- \frac{z}{4} = - \frac{4}{2 \cdot 4} - \frac{7}{8}$

Multiply $2$ by $4$ .

$- \frac{z}{4} = - \frac{4}{8} - \frac{7}{8}$

Combine the numerators over the common denominator.

$- \frac{z}{4} = \frac{- 4 - 7}{8}$

Subtract $7$ from $- 4$ .

$- \frac{z}{4} = \frac{- 11}{8}$

Move the negative in front of the fraction.

$- \frac{z}{4} = - \frac{11}{8}$

Step 3

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{z}{4}) = - 4 (- \frac{11}{8})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 4 (- \frac{z}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{z}{4}$ into the numerator.

$- 4 \frac{- z}{4} = - 4 (- \frac{11}{8})$

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- z}{4} = - 4 (- \frac{11}{8})$

Cancel the common factor.

$4 \cdot - 1 \frac{- z}{4} = - 4 (- \frac{11}{8})$

Rewrite the expression.

$- - z = - 4 (- \frac{11}{8})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 z = - 4 (- \frac{11}{8})$

Multiply $z$ by $1$ .

$z = - 4 (- \frac{11}{8})$

Simplify the right side.

Simplify $- 4 (- \frac{11}{8})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{11}{8}$ into the numerator.

$z = - 4 (\frac{- 11}{8})$

Factor $4$ out of $- 4$ .

$z = 4 (- 1) \frac{- 11}{8}$

Factor $4$ out of $8$ .

$z = 4 \cdot - 1 \frac{- 11}{4 \cdot 2}$

Cancel the common factor.

$z = 4 \cdot - 1 \frac{- 11}{4 \cdot 2}$

Rewrite the expression.

$z = - \frac{- 11}{2}$

Move the negative in front of the fraction.

$z = - - \frac{11}{2}$

Multiply $- - \frac{11}{2}$ .

Multiply $- 1$ by $- 1$ .

$z = 1 (\frac{11}{2})$

Multiply $\frac{11}{2}$ by $1$ .

$z = \frac{11}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = \frac{11}{2}$

Decimal Form:

$z = 5.5$

Mixed Number Form:

$z = 5 \frac{1}{2}$

Solve for z -1/4z+7/8=-1/2

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