Finite Math Examples

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

Step 1

Simplify $- 2 (w + 3)$ .

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Step 1.1

Rewrite.

$0 + 0 - 2 (w + 3) = 3 (w + 4) + 7$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply $- 2$ by $3$ .

$- 2 w - 6 = 3 (w + 4) + 7$

Step 2

Simplify $3 (w + 4) + 7$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 2 w - 6 = 3 w + 3 \cdot 4 + 7$

Step 2.1.2

Multiply $3$ by $4$ .

$- 2 w - 6 = 3 w + 12 + 7$

Step 2.2

Add $12$ and $7$ .

$- 2 w - 6 = 3 w + 19$

Step 3

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

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Step 3.1

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

$- 2 w - 6 - 3 w = 19$

Step 3.2

Subtract $3 w$ from $- 2 w$ .

$- 5 w - 6 = 19$

Step 4

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

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Step 4.1

Add $6$ to both sides of the equation.

$- 5 w = 19 + 6$

Step 4.2

Add $19$ and $6$ .

$- 5 w = 25$

Step 5

Divide each term in $- 5 w = 25$ by $- 5$ and simplify.

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Step 5.1

Divide each term in $- 5 w = 25$ by $- 5$ .

$\frac{- 5 w}{- 5} = \frac{25}{- 5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 5 w}{- 5} = \frac{25}{- 5}$

Step 5.2.1.2

Divide $w$ by $1$ .

$w = \frac{25}{- 5}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $25$ by $- 5$ .

$w = - 5$