Basic Math Examples

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

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

Step 1

Since

w

$w$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

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

Step 2

Simplify

- 2 (4 w - 3) + 6 w

$- 2 (4 w - 3) + 6 w$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

- 2 (4 w) - 2 \cdot - 3 + 6 w = 3 (w + 4)

$- 2 (4 w) - 2 \cdot - 3 + 6 w = 3 (w + 4)$

Step 2.1.2

Multiply

4

$4$ by

- 2

$- 2$ .

- 8 w - 2 \cdot - 3 + 6 w = 3 (w + 4)

$- 8 w - 2 \cdot - 3 + 6 w = 3 (w + 4)$

Step 2.1.3

Multiply

- 2

$- 2$ by

- 3

$- 3$ .

- 8 w + 6 + 6 w = 3 (w + 4)

$- 8 w + 6 + 6 w = 3 (w + 4)$

- 8 w + 6 + 6 w = 3 (w + 4)

$- 8 w + 6 + 6 w = 3 (w + 4)$

Step 2.2

Add

- 8 w

$- 8 w$ and

6 w

$6 w$ .

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

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

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

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

Step 3

Simplify

3 (w + 4)

$3 (w + 4)$ .

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Step 3.1

Apply the distributive property.

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

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

Step 3.2

Multiply

3

$3$ by

4

$4$ .

- 2 w + 6 = 3 w + 12

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

- 2 w + 6 = 3 w + 12

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

Step 4

Move all terms containing

$w$ to the left side of the equation.

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Step 4.1

Subtract

$3 w$ from both sides of the equation.

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

Step 4.2

Subtract

$3 w$ from

$- 2 w$ .

$- 5 w + 6 = 12$

$- 5 w + 6 = 12$

Step 5

Move all terms not containing

$w$ to the right side of the equation.

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Step 5.1

Subtract

$6$ from both sides of the equation.

$- 5 w = 12 - 6$

Step 5.2

Subtract

$6$ from

$12$ .

$- 5 w = 6$

$- 5 w = 6$

Step 6

Divide each term in

$- 5 w = 6$ by

$- 5$ and simplify.

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Step 6.1

Divide each term in

$- 5 w = 6$ by

$- 5$ .

$\frac{- 5 w}{- 5} = \frac{6}{- 5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of

$- 5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 5 w}{- 5} = \frac{6}{- 5}$

Step 6.2.1.2

Divide

$w$ by

$1$ .

$w = \frac{6}{- 5}$

$w = \frac{6}{- 5}$

$w = \frac{6}{- 5}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$w = - \frac{6}{5}$

$w = - \frac{6}{5}$

$w = - \frac{6}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$w = - \frac{6}{5}$

Decimal Form:

$w = - 1.2$

Mixed Number Form:

$w = - 1 \frac{1}{5}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$