Algebra Examples

$\frac{3 a}{4} = \frac{13}{3} - \frac{a}{3}$

Step 1

Multiply both sides by $4$ .

$\frac{3 a}{4} \cdot 4 = (\frac{13}{3} - \frac{a}{3}) \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{3 a}{4} \cdot 4 = (\frac{13}{3} - \frac{a}{3}) \cdot 4$

Step 2.1.1.2

Rewrite the expression.

$3 a = (\frac{13}{3} - \frac{a}{3}) \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{13}{3} - \frac{a}{3}) \cdot 4$ .

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Step 2.2.1.1

Apply the distributive property.

$3 a = \frac{13}{3} \cdot 4 - \frac{a}{3} \cdot 4$

Step 2.2.1.2

Multiply $\frac{13}{3} \cdot 4$ .

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Step 2.2.1.2.1

Combine $\frac{13}{3}$ and $4$ .

$3 a = \frac{13 \cdot 4}{3} - \frac{a}{3} \cdot 4$

Step 2.2.1.2.2

Multiply $13$ by $4$ .

$3 a = \frac{52}{3} - \frac{a}{3} \cdot 4$

Step 2.2.1.3

Multiply $- \frac{a}{3} \cdot 4$ .

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Step 2.2.1.3.1

Multiply $4$ by $- 1$ .

$3 a = \frac{52}{3} - 4 \frac{a}{3}$

Step 2.2.1.3.2

Combine $- 4$ and $\frac{a}{3}$ .

$3 a = \frac{52}{3} + \frac{- 4 a}{3}$

Step 2.2.1.4

Move the negative in front of the fraction.

$3 a = \frac{52}{3} - \frac{4 a}{3}$

Step 2.2.1.5

Reorder $\frac{52}{3}$ and $- \frac{4 a}{3}$ .

$3 a = - \frac{4 a}{3} + \frac{52}{3}$

Step 3

Solve for $a$ .

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Step 3.1

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

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Step 3.1.1

Add $\frac{4 a}{3}$ to both sides of the equation.

$3 a + \frac{4 a}{3} = \frac{52}{3}$

Step 3.1.2

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

$3 a \cdot \frac{3}{3} + \frac{4 a}{3} = \frac{52}{3}$

Step 3.1.3

Combine $3 a$ and $\frac{3}{3}$ .

$\frac{3 a \cdot 3}{3} + \frac{4 a}{3} = \frac{52}{3}$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{3 a \cdot 3 + 4 a}{3} = \frac{52}{3}$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Factor $a$ out of $3 a \cdot 3 + 4 a$ .

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Step 3.1.5.1.1

Factor $a$ out of $3 a \cdot 3$ .

$\frac{a (3 \cdot 3) + 4 a}{3} = \frac{52}{3}$

Step 3.1.5.1.2

Factor $a$ out of $4 a$ .

$\frac{a (3 \cdot 3) + a \cdot 4}{3} = \frac{52}{3}$

Step 3.1.5.1.3

Factor $a$ out of $a (3 \cdot 3) + a \cdot 4$ .

$\frac{a (3 \cdot 3 + 4)}{3} = \frac{52}{3}$

Step 3.1.5.2

Multiply $3$ by $3$ .

$\frac{a (9 + 4)}{3} = \frac{52}{3}$

Step 3.1.5.3

Add $9$ and $4$ .

$\frac{a \cdot 13}{3} = \frac{52}{3}$

Step 3.1.6

Move $13$ to the left of $a$ .

$\frac{13 a}{3} = \frac{52}{3}$

Step 3.2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$13 a = 52$

Step 3.3

Divide each term in $13 a = 52$ by $13$ and simplify.

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Step 3.3.1

Divide each term in $13 a = 52$ by $13$ .

$\frac{13 a}{13} = \frac{52}{13}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $13$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{13 a}{13} = \frac{52}{13}$

Step 3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{52}{13}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $52$ by $13$ .

$a = 4$