Algebra Examples

$2 (v - 3) = 1 - (w + 4)$

Step 1

Rewrite the equation as $1 - (w + 4) = 2 (v - 3)$ .

$1 - (w + 4) = 2 (v - 3)$

Step 2

Simplify $1 - (w + 4)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$1 - w - 1 \cdot 4 = 2 (v - 3)$

Step 2.1.2

Multiply $- 1$ by $4$ .

$1 - w - 4 = 2 (v - 3)$

Step 2.2

Subtract $4$ from $1$ .

$- w - 3 = 2 (v - 3)$

Step 3

Simplify $2 (v - 3)$ .

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Step 3.1

Apply the distributive property.

$- w - 3 = 2 v + 2 \cdot - 3$

Step 3.2

Multiply $2$ by $- 3$ .

$- w - 3 = 2 v - 6$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$- w = 2 v - 6 + 3$

Step 4.2

Add $- 6$ and $3$ .

$- w = 2 v - 3$

Step 5

Divide each term in $- w = 2 v - 3$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- w = 2 v - 3$ by $- 1$ .

$\frac{- w}{- 1} = \frac{2 v}{- 1} + \frac{- 3}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{w}{1} = \frac{2 v}{- 1} + \frac{- 3}{- 1}$

Step 5.2.2

Divide $w$ by $1$ .

$w = \frac{2 v}{- 1} + \frac{- 3}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Move the negative one from the denominator of $\frac{2 v}{- 1}$ .

$w = - 1 \cdot (2 v) + \frac{- 3}{- 1}$

Step 5.3.1.2

Rewrite $- 1 \cdot (2 v)$ as $- (2 v)$ .

$w = - (2 v) + \frac{- 3}{- 1}$

Step 5.3.1.3

Multiply $2$ by $- 1$ .

$w = - 2 v + \frac{- 3}{- 1}$

Step 5.3.1.4

Divide $- 3$ by $- 1$ .

$w = - 2 v + 3$