Solve for w 1/2w+7=2w-2

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

Step 1

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

$\frac{w}{2} + 7 = 2 w - 2$

Step 2

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

Subtract $2 w$ from both sides of the equation.

$\frac{w}{2} + 7 - 2 w = - 2$

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $w$ out of $w - 2 w \cdot 2$ .

Raise $w$ to the power of $1$ .

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

Factor $w$ out of $w^{1}$ .

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

Factor $w$ out of $- 2 w \cdot 2$ .

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

Factor $w$ out of $w \cdot 1 + w (- 2 \cdot 2)$ .

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

Multiply $- 2$ by $2$ .

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

Subtract $4$ from $1$ .

$\frac{w \cdot - 3}{2} + 7 = - 2$

Move $- 3$ to the left of $w$ .

$\frac{- 3 \cdot w}{2} + 7 = - 2$

Move the negative in front of the fraction.

$- \frac{3 w}{2} + 7 = - 2$

Step 3

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

Subtract $7$ from both sides of the equation.

$- \frac{3 w}{2} = - 2 - 7$

Subtract $7$ from $- 2$ .

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

Step 4

Multiply both sides of the equation by $- \frac{2}{3}$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

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

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

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

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

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 w}{2} = - \frac{2}{3} \cdot - 9$

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 w}{2} = - \frac{2}{3} \cdot - 9$

Rewrite the expression.

$\frac{- 1}{3} (- 3 w) = - \frac{2}{3} \cdot - 9$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 w$ .

$\frac{- 1}{3} (3 (- w)) = - \frac{2}{3} \cdot - 9$

Cancel the common factor.

$\frac{- 1}{3} (3 (- w)) = - \frac{2}{3} \cdot - 9$

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 w = - \frac{2}{3} \cdot - 9$

Multiply $w$ by $1$ .

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

Simplify the right side.

Simplify $- \frac{2}{3} \cdot - 9$ .

Cancel the common factor of $3$ .

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

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

Factor $3$ out of $- 9$ .

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

Cancel the common factor.

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

Rewrite the expression.

$w = - 2 \cdot - 3$

Multiply $- 2$ by $- 3$ .

$w = 6$

Solve for w 1/2w+7=2w-2

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