Solve for w 19-2(3w-5)=15

$19 - 2 (3 w - 5) = 15$

Step 1

Simplify $19 - 2 (3 w - 5)$ .

Simplify each term.

Apply the distributive property.

$19 - 2 (3 w) - 2 \cdot - 5 = 15$

Multiply $3$ by $- 2$ .

$19 - 6 w - 2 \cdot - 5 = 15$

Multiply $- 2$ by $- 5$ .

$19 - 6 w + 10 = 15$

Add $19$ and $10$ .

$- 6 w + 29 = 15$

Step 2

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

Subtract $29$ from both sides of the equation.

$- 6 w = 15 - 29$

Subtract $29$ from $15$ .

$- 6 w = - 14$

Step 3

Divide each term in $- 6 w = - 14$ by $- 6$ and simplify.

Divide each term in $- 6 w = - 14$ by $- 6$ .

$\frac{- 6 w}{- 6} = \frac{- 14}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 w}{- 6} = \frac{- 14}{- 6}$

Divide $w$ by $1$ .

$w = \frac{- 14}{- 6}$

Simplify the right side.

Cancel the common factor of $- 14$ and $- 6$ .

Factor $- 2$ out of $- 14$ .

$w = \frac{- 2 (7)}{- 6}$

Cancel the common factors.

Factor $- 2$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$w = 2.\overline{3}$

Mixed Number Form:

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

Solve for w 19-2(3w-5)=15

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