Algebra Examples

$\frac{1}{3} (\frac{3}{4} e - 12) + 3 e = 6 - \frac{1}{2} e$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{1}{3} \cdot (\frac{3 e}{4} - 12) + 3 e = 6 - \frac{1}{2} \cdot e$

Step 1.2

Apply the distributive property.

$\frac{1}{3} \cdot \frac{3 e}{4} + \frac{1}{3} \cdot - 12 + 3 e = 6 - \frac{1}{2} \cdot e$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Factor $3$ out of $3 e$ .

$\frac{1}{3} \cdot \frac{3 (e)}{4} + \frac{1}{3} \cdot - 12 + 3 e = 6 - \frac{1}{2} \cdot e$

Step 1.3.2

Cancel the common factor.

$\frac{1}{3} \cdot \frac{3 e}{4} + \frac{1}{3} \cdot - 12 + 3 e = 6 - \frac{1}{2} \cdot e$

Step 1.3.3

Rewrite the expression.

$\frac{e}{4} + \frac{1}{3} \cdot - 12 + 3 e = 6 - \frac{1}{2} \cdot e$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $- 12$ .

$\frac{e}{4} + \frac{1}{3} \cdot (3 (- 4)) + 3 e = 6 - \frac{1}{2} \cdot e$

Step 1.4.2

Cancel the common factor.

$\frac{e}{4} + \frac{1}{3} \cdot (3 \cdot - 4) + 3 e = 6 - \frac{1}{2} \cdot e$

Step 1.4.3

Rewrite the expression.

$\frac{e}{4} - 4 + 3 e = 6 - \frac{1}{2} \cdot e$

Step 2

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

$\frac{e}{4} + 3 e \cdot \frac{4}{4} - 4 = 6 - \frac{1}{2} \cdot e$

Step 3

Combine fractions.

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Step 3.1

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

$\frac{e}{4} + \frac{3 e \cdot 4}{4} - 4 = 6 - \frac{1}{2} \cdot e$

Step 3.2

Combine the numerators over the common denominator.

$\frac{e + 3 e \cdot 4}{4} - 4 = 6 - \frac{1}{2} \cdot e$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $4$ by $3$ .

$\frac{e + 12 e}{4} - 4 = 6 - \frac{1}{2} \cdot e$

Step 4.2

Add $e$ and $12 e$ .

$\frac{13 e}{4} - 4 = 6 - \frac{1}{2} \cdot e$

Step 5

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

$\frac{13 e}{4} - 4 = 6 - \frac{e}{2}$