Algebra Examples

$w - 2 (w + 5 (1 - 2 w) + 4 w) - (w + 3) = - w + 3 (w + 2) + 7 w$

Step 1

Simplify $w - 2 (w + 5 (1 - 2 w) + 4 w) - (w + 3)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Simplify each term.

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Step 1.1.1.1

Apply the distributive property.

$w - 2 (w + 5 \cdot 1 + 5 (- 2 w) + 4 w) - (w + 3) = - w + 3 (w + 2) + 7 w$

Step 1.1.1.2

Multiply $5$ by $1$ .

$w - 2 (w + 5 + 5 (- 2 w) + 4 w) - (w + 3) = - w + 3 (w + 2) + 7 w$

Step 1.1.1.3

Multiply $- 2$ by $5$ .

$w - 2 (w + 5 - 10 w + 4 w) - (w + 3) = - w + 3 (w + 2) + 7 w$

Step 1.1.2

Subtract $10 w$ from $w$ .

$w - 2 (- 9 w + 5 + 4 w) - (w + 3) = - w + 3 (w + 2) + 7 w$

Step 1.1.3

Add $- 9 w$ and $4 w$ .

$w - 2 (- 5 w + 5) - (w + 3) = - w + 3 (w + 2) + 7 w$

Step 1.1.4

Apply the distributive property.

$w - 2 (- 5 w) - 2 \cdot 5 - (w + 3) = - w + 3 (w + 2) + 7 w$

Step 1.1.5

Multiply $- 5$ by $- 2$ .

$w + 10 w - 2 \cdot 5 - (w + 3) = - w + 3 (w + 2) + 7 w$

Step 1.1.6

Multiply $- 2$ by $5$ .

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

Step 1.1.7

Apply the distributive property.

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

Step 1.1.8

Multiply $- 1$ by $3$ .

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

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $w + 10 w - 10 - w - 3$ .

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Step 1.2.1.1

Subtract $w$ from $w$ .

$10 w - 10 + 0 - 3 = - w + 3 (w + 2) + 7 w$

Step 1.2.1.2

Add $10 w - 10$ and $0$ .

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

Step 1.2.2

Subtract $3$ from $- 10$ .

$10 w - 13 = - w + 3 (w + 2) + 7 w$

Step 2

Simplify $- w + 3 (w + 2) + 7 w$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$10 w - 13 = - w + 3 w + 3 \cdot 2 + 7 w$

Step 2.1.2

Multiply $3$ by $2$ .

$10 w - 13 = - w + 3 w + 6 + 7 w$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $- w$ and $3 w$ .

$10 w - 13 = 2 w + 6 + 7 w$

Step 2.2.2

Add $2 w$ and $7 w$ .

$10 w - 13 = 9 w + 6$

Step 3

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

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Step 3.1

Subtract $9 w$ from both sides of the equation.

$10 w - 13 - 9 w = 6$

Step 3.2

Subtract $9 w$ from $10 w$ .

$w - 13 = 6$

Step 4

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

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Step 4.1

Add $13$ to both sides of the equation.

$w = 6 + 13$

Step 4.2

Add $6$ and $13$ .

$w = 19$