Algebra Examples

$9 + 3 = 12 + \frac{v - 8}{2}$

Step 1

Rewrite the equation as $12 + \frac{v - 8}{2} = 9 + 3$ .

$12 + \frac{v - 8}{2} = 9 + 3$

Step 2

Simplify $12 + \frac{v - 8}{2}$ .

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Step 2.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$12 \cdot \frac{2}{2} + \frac{v - 8}{2} = 9 + 3$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine $12$ and $\frac{2}{2}$ .

$\frac{12 \cdot 2}{2} + \frac{v - 8}{2} = 9 + 3$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{12 \cdot 2 + v - 8}{2} = 9 + 3$

Step 2.3

Simplify the numerator.

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Step 2.3.1

Multiply $12$ by $2$ .

$\frac{24 + v - 8}{2} = 9 + 3$

Step 2.3.2

Subtract $8$ from $24$ .

$\frac{v + 16}{2} = 9 + 3$

Step 3

Add $9$ and $3$ .

$\frac{v + 16}{2} = 12$

Step 4

Multiply both sides of the equation by $2$ .

$2 \frac{v + 16}{2} = 2 \cdot 12$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1

Cancel the common factor.

$2 \frac{v + 16}{2} = 2 \cdot 12$

Step 5.1.1.2

Rewrite the expression.

$v + 16 = 2 \cdot 12$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $2$ by $12$ .

$v + 16 = 24$

Step 6

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

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Step 6.1

Subtract $16$ from both sides of the equation.

$v = 24 - 16$

Step 6.2

Subtract $16$ from $24$ .

$v = 8$