Basic Math Examples

$18 = \frac{5 v - 8}{3} + \frac{v + 6}{4}$

Step 1

Rewrite the equation as $\frac{5 v - 8}{3} + \frac{v + 6}{4} = 18$ .

$\frac{5 v - 8}{3} + \frac{v + 6}{4} = 18$

Step 2

Simplify $\frac{5 v - 8}{3} + \frac{v + 6}{4}$ .

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Step 2.1

To write $\frac{5 v - 8}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 v - 8}{3} \cdot \frac{4}{4} + \frac{v + 6}{4} = 18$

Step 2.2

To write $\frac{v + 6}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 v - 8}{3} \cdot \frac{4}{4} + \frac{v + 6}{4} \cdot \frac{3}{3} = 18$

Step 2.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{5 v - 8}{3}$ by $\frac{4}{4}$ .

$\frac{(5 v - 8) \cdot 4}{3 \cdot 4} + \frac{v + 6}{4} \cdot \frac{3}{3} = 18$

Step 2.3.2

Multiply $3$ by $4$ .

$\frac{(5 v - 8) \cdot 4}{12} + \frac{v + 6}{4} \cdot \frac{3}{3} = 18$

Step 2.3.3

Multiply $\frac{v + 6}{4}$ by $\frac{3}{3}$ .

$\frac{(5 v - 8) \cdot 4}{12} + \frac{(v + 6) \cdot 3}{4 \cdot 3} = 18$

Step 2.3.4

Multiply $4$ by $3$ .

$\frac{(5 v - 8) \cdot 4}{12} + \frac{(v + 6) \cdot 3}{12} = 18$

Step 2.4

Combine the numerators over the common denominator.

$\frac{(5 v - 8) \cdot 4 + (v + 6) \cdot 3}{12} = 18$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Apply the distributive property.

$\frac{5 v \cdot 4 - 8 \cdot 4 + (v + 6) \cdot 3}{12} = 18$

Step 2.5.2

Multiply $4$ by $5$ .

$\frac{20 v - 8 \cdot 4 + (v + 6) \cdot 3}{12} = 18$

Step 2.5.3

Multiply $- 8$ by $4$ .

$\frac{20 v - 32 + (v + 6) \cdot 3}{12} = 18$

Step 2.5.4

Apply the distributive property.

$\frac{20 v - 32 + v \cdot 3 + 6 \cdot 3}{12} = 18$

Step 2.5.5

Move $3$ to the left of $v$ .

$\frac{20 v - 32 + 3 \cdot v + 6 \cdot 3}{12} = 18$

Step 2.5.6

Multiply $6$ by $3$ .

$\frac{20 v - 32 + 3 \cdot v + 18}{12} = 18$

Step 2.5.7

Add $20 v$ and $3 v$ .

$\frac{23 v - 32 + 18}{12} = 18$

Step 2.5.8

Add $- 32$ and $18$ .

$\frac{23 v - 14}{12} = 18$

Step 3

Multiply both sides by $12$ .

$\frac{23 v - 14}{12} \cdot 12 = 18 \cdot 12$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $12$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{23 v - 14}{12} \cdot 12 = 18 \cdot 12$

Step 4.1.1.2

Rewrite the expression.

$23 v - 14 = 18 \cdot 12$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $18$ by $12$ .

$23 v - 14 = 216$

Step 5

Solve for $v$ .

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Step 5.1

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

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Step 5.1.1

Add $14$ to both sides of the equation.

$23 v = 216 + 14$

Step 5.1.2

Add $216$ and $14$ .

$23 v = 230$

Step 5.2

Divide each term in $23 v = 230$ by $23$ and simplify.

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Step 5.2.1

Divide each term in $23 v = 230$ by $23$ .

$\frac{23 v}{23} = \frac{230}{23}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $23$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{23 v}{23} = \frac{230}{23}$

Step 5.2.2.1.2

Divide $v$ by $1$ .

$v = \frac{230}{23}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $230$ by $23$ .

$v = 10$