Algebra Examples

$7 w = \frac{1}{2} (w + v)$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (w + v) = 7 w$ .

$\frac{1}{2} \cdot (w + v) = 7 w$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (w + v)) = 2 (7 w)$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $2 (\frac{1}{2} \cdot (w + v))$ .

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Step 3.1.1.1

Apply the distributive property.

$2 (\frac{1}{2} w + \frac{1}{2} v) = 2 (7 w)$

Step 3.1.1.2

Combine $\frac{1}{2}$ and $w$ .

$2 (\frac{w}{2} + \frac{1}{2} v) = 2 (7 w)$

Step 3.1.1.3

Combine $\frac{1}{2}$ and $v$ .

$2 (\frac{w}{2} + \frac{v}{2}) = 2 (7 w)$

Step 3.1.1.4

Apply the distributive property.

$2 \frac{w}{2} + 2 \frac{v}{2} = 2 (7 w)$

Step 3.1.1.5

Cancel the common factor of $2$ .

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Step 3.1.1.5.1

Cancel the common factor.

$2 \frac{w}{2} + 2 \frac{v}{2} = 2 (7 w)$

Step 3.1.1.5.2

Rewrite the expression.

$w + 2 \frac{v}{2} = 2 (7 w)$

$w + 2 \frac{v}{2} = 2 (7 w)$

Step 3.1.1.6

Cancel the common factor of $2$ .

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Step 3.1.1.6.1

Cancel the common factor.

$w + 2 \frac{v}{2} = 2 (7 w)$

Step 3.1.1.6.2

Rewrite the expression.

$w + v = 2 (7 w)$

$w + v = 2 (7 w)$

$w + v = 2 (7 w)$

$w + v = 2 (7 w)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $7$ by $2$ .

$w + v = 14 w$

$w + v = 14 w$

$w + v = 14 w$

Step 4

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

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Step 4.1

Subtract $w$ from both sides of the equation.

$v = 14 w - w$

Step 4.2

Subtract $w$ from $14 w$ .

$v = 13 w$

$v = 13 w$

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