Solve for w 12w-27=-34+14w

$12 w - 27 = - 34 + 14 w$

Step 1

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

Subtract $14 w$ from both sides of the equation.

$12 w - 27 - 14 w = - 34$

Subtract $14 w$ from $12 w$ .

$- 2 w - 27 = - 34$

Step 2

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

Add $27$ to both sides of the equation.

$- 2 w = - 34 + 27$

Add $- 34$ and $27$ .

$- 2 w = - 7$

Step 3

Divide each term in $- 2 w = - 7$ by $- 2$ and simplify.

Divide each term in $- 2 w = - 7$ by $- 2$ .

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $w$ by $1$ .

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

Simplify the right side.

Dividing two negative values results in a positive value.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$w = 3.5$

Mixed Number Form:

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