Pre-Algebra Examples

$3 (w - (10 - w)) = 7 (w + 1)$

Step 1

Simplify $3 (w - (10 - w))$ .

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Step 1.1

Rewrite.

$0 + 0 + 3 (w - (10 - w)) = 7 (w + 1)$

Step 1.2

Simplify by adding zeros.

$3 (w - (10 - w)) = 7 (w + 1)$

Step 1.3

Simplify each term.

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Step 1.3.1

Apply the distributive property.

$3 (w - 1 \cdot 10 - - w) = 7 (w + 1)$

Step 1.3.2

Multiply $- 1$ by $10$ .

$3 (w - 10 - - w) = 7 (w + 1)$

Step 1.3.3

Multiply $- - w$ .

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Step 1.3.3.1

Multiply $- 1$ by $- 1$ .

$3 (w - 10 + 1 w) = 7 (w + 1)$

Step 1.3.3.2

Multiply $w$ by $1$ .

$3 (w - 10 + w) = 7 (w + 1)$

Step 1.4

Simplify terms.

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Step 1.4.1

Add $w$ and $w$ .

$3 (2 w - 10) = 7 (w + 1)$

Step 1.4.2

Apply the distributive property.

$3 (2 w) + 3 \cdot - 10 = 7 (w + 1)$

Step 1.4.3

Multiply.

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Step 1.4.3.1

Multiply $2$ by $3$ .

$6 w + 3 \cdot - 10 = 7 (w + 1)$

Step 1.4.3.2

Multiply $3$ by $- 10$ .

$6 w - 30 = 7 (w + 1)$

Step 2

Simplify $7 (w + 1)$ .

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Step 2.1

Apply the distributive property.

$6 w - 30 = 7 w + 7 \cdot 1$

Step 2.2

Multiply $7$ by $1$ .

$6 w - 30 = 7 w + 7$

Step 3

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

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Step 3.1

Subtract $7 w$ from both sides of the equation.

$6 w - 30 - 7 w = 7$

Step 3.2

Subtract $7 w$ from $6 w$ .

$- w - 30 = 7$

Step 4

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

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Step 4.1

Add $30$ to both sides of the equation.

$- w = 7 + 30$

Step 4.2

Add $7$ and $30$ .

$- w = 37$

Step 5

Divide each term in $- w = 37$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- w = 37$ by $- 1$ .

$\frac{- w}{- 1} = \frac{37}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{w}{1} = \frac{37}{- 1}$

Step 5.2.2

Divide $w$ by $1$ .

$w = \frac{37}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $37$ by $- 1$ .

$w = - 37$