Algebra Examples

$9 (2 + w) - 4 w = 3 w - 10$

Step 1

Simplify $9 (2 + w) - 4 w$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$9 \cdot 2 + 9 w - 4 w = 3 w - 10$

Step 1.1.2

Multiply $9$ by $2$ .

$18 + 9 w - 4 w = 3 w - 10$

Step 1.2

Subtract $4 w$ from $9 w$ .

$18 + 5 w = 3 w - 10$

Step 2

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

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Step 2.1

Subtract $3 w$ from both sides of the equation.

$18 + 5 w - 3 w = - 10$

Step 2.2

Subtract $3 w$ from $5 w$ .

$18 + 2 w = - 10$

Step 3

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

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Step 3.1

Subtract $18$ from both sides of the equation.

$2 w = - 10 - 18$

Step 3.2

Subtract $18$ from $- 10$ .

$2 w = - 28$

Step 4

Divide each term in $2 w = - 28$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 w = - 28$ by $2$ .

$\frac{2 w}{2} = \frac{- 28}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 w}{2} = \frac{- 28}{2}$

Step 4.2.1.2

Divide $w$ by $1$ .

$w = \frac{- 28}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 28$ by $2$ .

$w = - 14$