Solve for w 6/5w=3-3(1/2w+3/2)

$\frac{6}{5} w = 3 - 3 (\frac{1}{2} w + \frac{3}{2})$

Simplify $\frac{6}{5} w$ .

Rewrite.

$0 + 0 + \frac{6}{5} w = 3 - 3 (\frac{1}{2} w + \frac{3}{2})$

Simplify by adding zeros.

$\frac{6}{5} w = 3 - 3 (\frac{1}{2} w + \frac{3}{2})$

Combine $\frac{6}{5}$ and $w$ .

$\frac{6 w}{5} = 3 - 3 (\frac{1}{2} w + \frac{3}{2})$

Simplify $3 - 3 (\frac{1}{2} w + \frac{3}{2})$ .

Simplify each term.

Combine $\frac{1}{2}$ and $w$ .

$\frac{6 w}{5} = 3 - 3 (\frac{w}{2} + \frac{3}{2})$

Apply the distributive property.

$\frac{6 w}{5} = 3 - 3 \frac{w}{2} - 3 (\frac{3}{2})$

Combine $- 3$ and $\frac{w}{2}$ .

$\frac{6 w}{5} = 3 + \frac{- 3 w}{2} - 3 (\frac{3}{2})$

Multiply $- 3 (\frac{3}{2})$ .

Combine $- 3$ and $\frac{3}{2}$ .

$\frac{6 w}{5} = 3 + \frac{- 3 w}{2} + \frac{- 3 \cdot 3}{2}$

Multiply $- 3$ by $3$ .

$\frac{6 w}{5} = 3 + \frac{- 3 w}{2} + \frac{- 9}{2}$

Simplify each term.

Move the negative in front of the fraction.

$\frac{6 w}{5} = 3 - \frac{(3) w}{2} + \frac{- 9}{2}$

Move the negative in front of the fraction.

$\frac{6 w}{5} = 3 - \frac{3 w}{2} - \frac{9}{2}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{6 w}{5} = - \frac{3 w}{2} + 3 \cdot \frac{2}{2} - \frac{9}{2}$

Combine $3$ and $\frac{2}{2}$ .

$\frac{6 w}{5} = - \frac{3 w}{2} + \frac{3 \cdot 2}{2} - \frac{9}{2}$

Combine the numerators over the common denominator.

$\frac{6 w}{5} = - \frac{3 w}{2} + \frac{3 \cdot 2 - 9}{2}$

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{6 w}{5} = - \frac{3 w}{2} + \frac{6 - 9}{2}$

Subtract $9$ from $6$ .

$\frac{6 w}{5} = - \frac{3 w}{2} + \frac{- 3}{2}$

Move the negative in front of the fraction.

$\frac{6 w}{5} = - \frac{3 w}{2} - \frac{3}{2}$

Move all terms containing $w$ to the left side of the equation.

Add $\frac{3 w}{2}$ to both sides of the equation.

$\frac{6 w}{5} + \frac{3 w}{2} = - \frac{3}{2}$

To write $\frac{6 w}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{6 w}{5} \cdot \frac{2}{2} + \frac{3 w}{2} = - \frac{3}{2}$

To write $\frac{3 w}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{6 w}{5} \cdot \frac{2}{2} + \frac{3 w}{2} \cdot \frac{5}{5} = - \frac{3}{2}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{6 w}{5}$ by $\frac{2}{2}$ .

$\frac{6 w \cdot 2}{5 \cdot 2} + \frac{3 w}{2} \cdot \frac{5}{5} = - \frac{3}{2}$

Multiply $5$ by $2$ .

$\frac{6 w \cdot 2}{10} + \frac{3 w}{2} \cdot \frac{5}{5} = - \frac{3}{2}$

Multiply $\frac{3 w}{2}$ by $\frac{5}{5}$ .

$\frac{6 w \cdot 2}{10} + \frac{3 w \cdot 5}{2 \cdot 5} = - \frac{3}{2}$

Multiply $2$ by $5$ .

$\frac{6 w \cdot 2}{10} + \frac{3 w \cdot 5}{10} = - \frac{3}{2}$

Combine the numerators over the common denominator.

$\frac{6 w \cdot 2 + 3 w \cdot 5}{10} = - \frac{3}{2}$

Simplify the numerator.

Factor $3 w$ out of $6 w \cdot 2 + 3 w \cdot 5$ .

Factor $3 w$ out of $6 w \cdot 2$ .

$\frac{3 w (2 \cdot 2) + 3 w \cdot 5}{10} = - \frac{3}{2}$

Factor $3 w$ out of $3 w \cdot 5$ .

$\frac{3 w (2 \cdot 2) + 3 w (5)}{10} = - \frac{3}{2}$

Factor $3 w$ out of $3 w (2 \cdot 2) + 3 w (5)$ .

$\frac{3 w (2 \cdot 2 + 5)}{10} = - \frac{3}{2}$

Multiply $2$ by $2$ .

$\frac{3 w (4 + 5)}{10} = - \frac{3}{2}$

Add $4$ and $5$ .

$\frac{3 w \cdot 9}{10} = - \frac{3}{2}$

Multiply $9$ by $3$ .

$\frac{27 w}{10} = - \frac{3}{2}$

Multiply both sides of the equation by $\frac{10}{27}$ .

$\frac{10}{27} \cdot \frac{27 w}{10} = \frac{10}{27} (- \frac{3}{2})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{10}{27} \cdot \frac{27 w}{10}$ .

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10}{27} \cdot \frac{27 w}{10} = \frac{10}{27} (- \frac{3}{2})$

Rewrite the expression.

$\frac{1}{27} (27 w) = \frac{10}{27} (- \frac{3}{2})$

Cancel the common factor of $27$ .

Factor $27$ out of $27 w$ .

$\frac{1}{27} (27 (w)) = \frac{10}{27} (- \frac{3}{2})$

Cancel the common factor.

$\frac{1}{27} (27 w) = \frac{10}{27} (- \frac{3}{2})$

Rewrite the expression.

$w = \frac{10}{27} (- \frac{3}{2})$

Simplify the right side.

Simplify $\frac{10}{27} (- \frac{3}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$w = \frac{10}{27} \cdot \frac{- 3}{2}$

Factor $2$ out of $10$ .

$w = \frac{2 (5)}{27} \cdot \frac{- 3}{2}$

Cancel the common factor.

$w = \frac{2 \cdot 5}{27} \cdot \frac{- 3}{2}$

Rewrite the expression.

$w = \frac{5}{27} \cdot - 3$

Cancel the common factor of $3$ .

Factor $3$ out of $27$ .

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

Factor $3$ out of $- 3$ .

$w = \frac{5}{3 \cdot 9} \cdot (3 \cdot - 1)$

Cancel the common factor.

$w = \frac{5}{3 \cdot 9} \cdot (3 \cdot - 1)$

Rewrite the expression.

$w = \frac{5}{9} \cdot - 1$

Combine $\frac{5}{9}$ and $- 1$ .

$w = \frac{5 \cdot - 1}{9}$

Simplify the expression.

Multiply $5$ by $- 1$ .

$w = \frac{- 5}{9}$

Move the negative in front of the fraction.

$w = - \frac{5}{9}$

The result can be shown in multiple forms.

Exact Form:

$w = - \frac{5}{9}$

Decimal Form:

$w = - 0.\overline{5}$

Solve for w 6/5w=3-3(1/2w+3/2)

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