Solve for w -2(w-7)+10w=34

$- 2 (w - 7) + 10 w = 34$

Simplify $- 2 (w - 7) + 10 w$ .

Simplify each term.

Apply the distributive property.

$- 2 w - 2 \cdot - 7 + 10 w = 34$

Multiply $- 2$ by $- 7$ .

$- 2 w + 14 + 10 w = 34$

Add $- 2 w$ and $10 w$ .

$8 w + 14 = 34$

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

Subtract $14$ from both sides of the equation.

$8 w = 34 - 14$

Subtract $14$ from $34$ .

$8 w = 20$

Divide each term in $8 w = 20$ by $8$ and simplify.

Divide each term in $8 w = 20$ by $8$ .

$\frac{8 w}{8} = \frac{20}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 w}{8} = \frac{20}{8}$

Divide $w$ by $1$ .

$w = \frac{20}{8}$

Simplify the right side.

Cancel the common factor of $20$ and $8$ .

Factor $4$ out of $20$ .

$w = \frac{4 (5)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$w = \frac{4 \cdot 5}{4 \cdot 2}$

Cancel the common factor.

$w = \frac{4 \cdot 5}{4 \cdot 2}$

Rewrite the expression.

$w = \frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$w = \frac{5}{2}$

Decimal Form:

$w = 2.5$

Mixed Number Form:

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