Solve for w 9/4(w-1/9)=7/2

$\frac{9}{4} (w - \frac{1}{9}) = \frac{7}{2}$

Multiply both sides of the equation by $\frac{4}{9}$ .

$\frac{4}{9} (\frac{9}{4} \cdot (w - \frac{1}{9})) = \frac{4}{9} \cdot \frac{7}{2}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{9} (\frac{9}{4} \cdot (w - \frac{1}{9}))$ .

Apply the distributive property.

$\frac{4}{9} (\frac{9}{4} w + \frac{9}{4} (- \frac{1}{9})) = \frac{4}{9} \cdot \frac{7}{2}$

Combine $\frac{9}{4}$ and $w$ .

$\frac{4}{9} (\frac{9 w}{4} + \frac{9}{4} (- \frac{1}{9})) = \frac{4}{9} \cdot \frac{7}{2}$

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{1}{9}$ into the numerator.

$\frac{4}{9} (\frac{9 w}{4} + \frac{9}{4} \cdot \frac{- 1}{9}) = \frac{4}{9} \cdot \frac{7}{2}$

Cancel the common factor.

$\frac{4}{9} (\frac{9 w}{4} + \frac{9}{4} \cdot \frac{- 1}{9}) = \frac{4}{9} \cdot \frac{7}{2}$

Rewrite the expression.

$\frac{4}{9} (\frac{9 w}{4} + \frac{1}{4} \cdot - 1) = \frac{4}{9} \cdot \frac{7}{2}$

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

$\frac{4}{9} (\frac{9 w}{4} + \frac{- 1}{4}) = \frac{4}{9} \cdot \frac{7}{2}$

Move the negative in front of the fraction.

$\frac{4}{9} (\frac{9 w}{4} - \frac{1}{4}) = \frac{4}{9} \cdot \frac{7}{2}$

Apply the distributive property.

$\frac{4}{9} \cdot \frac{9 w}{4} + \frac{4}{9} (- \frac{1}{4}) = \frac{4}{9} \cdot \frac{7}{2}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{9} \cdot \frac{9 w}{4} + \frac{4}{9} (- \frac{1}{4}) = \frac{4}{9} \cdot \frac{7}{2}$

Rewrite the expression.

$\frac{1}{9} (9 w) + \frac{4}{9} (- \frac{1}{4}) = \frac{4}{9} \cdot \frac{7}{2}$

Cancel the common factor of $9$ .

Factor $9$ out of $9 w$ .

$\frac{1}{9} (9 (w)) + \frac{4}{9} (- \frac{1}{4}) = \frac{4}{9} \cdot \frac{7}{2}$

Cancel the common factor.

$\frac{1}{9} (9 w) + \frac{4}{9} (- \frac{1}{4}) = \frac{4}{9} \cdot \frac{7}{2}$

Rewrite the expression.

$w + \frac{4}{9} (- \frac{1}{4}) = \frac{4}{9} \cdot \frac{7}{2}$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$w + \frac{4}{9} \cdot \frac{- 1}{4} = \frac{4}{9} \cdot \frac{7}{2}$

Cancel the common factor.

$w + \frac{4}{9} \cdot \frac{- 1}{4} = \frac{4}{9} \cdot \frac{7}{2}$

Rewrite the expression.

$w + \frac{1}{9} \cdot - 1 = \frac{4}{9} \cdot \frac{7}{2}$

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

$w + \frac{- 1}{9} = \frac{4}{9} \cdot \frac{7}{2}$

Move the negative in front of the fraction.

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

Simplify the right side.

Simplify $\frac{4}{9} \cdot \frac{7}{2}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$w - \frac{1}{9} = \frac{2 (2)}{9} \cdot \frac{7}{2}$

Cancel the common factor.

$w - \frac{1}{9} = \frac{2 \cdot 2}{9} \cdot \frac{7}{2}$

Rewrite the expression.

$w - \frac{1}{9} = \frac{2}{9} \cdot 7$

Combine $\frac{2}{9}$ and $7$ .

$w - \frac{1}{9} = \frac{2 \cdot 7}{9}$

Multiply $2$ by $7$ .

$w - \frac{1}{9} = \frac{14}{9}$

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

Add $\frac{1}{9}$ to both sides of the equation.

$w = \frac{14}{9} + \frac{1}{9}$

Combine the numerators over the common denominator.

$w = \frac{14 + 1}{9}$

Add $14$ and $1$ .

$w = \frac{15}{9}$

Cancel the common factor of $15$ and $9$ .

Factor $3$ out of $15$ .

$w = \frac{3 (5)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

$w = \frac{3 \cdot 5}{3 \cdot 3}$

Cancel the common factor.

$w = \frac{3 \cdot 5}{3 \cdot 3}$

Rewrite the expression.

$w = \frac{5}{3}$

The result can be shown in multiple forms.

Exact Form:

$w = \frac{5}{3}$

Decimal Form:

$w = 1.\overline{6}$

Mixed Number Form:

$w = 1 \frac{2}{3}$

Solve for w 9/4(w-1/9)=7/2

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