Solve for x 7/8=1/4-1/9x

$\frac{7}{8} = \frac{1}{4} - \frac{1}{9} x$

Rewrite the equation as $\frac{1}{4} - \frac{1}{9} x = \frac{7}{8}$ .

$\frac{1}{4} - \frac{1}{9} x = \frac{7}{8}$

Combine $x$ and $\frac{1}{9}$ .

$\frac{1}{4} - \frac{x}{9} = \frac{7}{8}$

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

Subtract $\frac{1}{4}$ from both sides of the equation.

$- \frac{x}{9} = \frac{7}{8} - \frac{1}{4}$

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

$- \frac{x}{9} = \frac{7}{8} - \frac{1}{4} \cdot \frac{2}{2}$

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

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

$- \frac{x}{9} = \frac{7}{8} - \frac{2}{4 \cdot 2}$

Multiply $4$ by $2$ .

$- \frac{x}{9} = \frac{7}{8} - \frac{2}{8}$

Combine the numerators over the common denominator.

$- \frac{x}{9} = \frac{7 - 2}{8}$

Subtract $2$ from $7$ .

$- \frac{x}{9} = \frac{5}{8}$

Multiply both sides of the equation by $- 9$ .

$- 9 (- \frac{x}{9}) = - 9 (\frac{5}{8})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 9 (- \frac{x}{9})$ .

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{x}{9}$ into the numerator.

$- 9 \frac{- x}{9} = - 9 (\frac{5}{8})$

Factor $9$ out of $- 9$ .

$9 (- 1) \frac{- x}{9} = - 9 (\frac{5}{8})$

Cancel the common factor.

$9 \cdot - 1 \frac{- x}{9} = - 9 (\frac{5}{8})$

Rewrite the expression.

$- - x = - 9 (\frac{5}{8})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 9 (\frac{5}{8})$

Multiply $x$ by $1$ .

$x = - 9 (\frac{5}{8})$

Simplify the right side.

Simplify $- 9 (\frac{5}{8})$ .

Multiply $- 9 (\frac{5}{8})$ .

Combine $- 9$ and $\frac{5}{8}$ .

$x = \frac{- 9 \cdot 5}{8}$

Multiply $- 9$ by $5$ .

$x = \frac{- 45}{8}$

Move the negative in front of the fraction.

$x = - \frac{45}{8}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{45}{8}$

Decimal Form:

$x = - 5.625$

Mixed Number Form:

$x = - 5 \frac{5}{8}$

Solve for x 7/8=1/4-1/9x

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