Algebra Examples

$\frac{1}{6} x + \frac{3}{4} (\frac{1}{2} x - 4)$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{6}$ and $x$ .

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

Step 1.2

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

$\frac{x}{6} + \frac{3}{4} \cdot (\frac{x}{2} - 4)$

Step 1.3

Apply the distributive property.

$\frac{x}{6} + \frac{3}{4} \cdot \frac{x}{2} + \frac{3}{4} \cdot - 4$

Step 1.4

Multiply $\frac{3}{4} \cdot \frac{x}{2}$ .

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Step 1.4.1

Multiply $\frac{3}{4}$ by $\frac{x}{2}$ .

$\frac{x}{6} + \frac{3 x}{4 \cdot 2} + \frac{3}{4} \cdot - 4$

Step 1.4.2

Multiply $4$ by $2$ .

$\frac{x}{6} + \frac{3 x}{8} + \frac{3}{4} \cdot - 4$

Step 1.5

Cancel the common factor of $4$ .

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Step 1.5.1

Factor $4$ out of $- 4$ .

$\frac{x}{6} + \frac{3 x}{8} + \frac{3}{4} \cdot (4 (- 1))$

Step 1.5.2

Cancel the common factor.

$\frac{x}{6} + \frac{3 x}{8} + \frac{3}{4} \cdot (4 \cdot - 1)$

Step 1.5.3

Rewrite the expression.

$\frac{x}{6} + \frac{3 x}{8} + 3 \cdot - 1$

Step 1.6

Multiply $3$ by $- 1$ .

$\frac{x}{6} + \frac{3 x}{8} - 3$

Step 2

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

$\frac{x}{6} \cdot \frac{4}{4} + \frac{3 x}{8} - 3$

Step 3

To write $\frac{3 x}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{6} \cdot \frac{4}{4} + \frac{3 x}{8} \cdot \frac{3}{3} - 3$

Step 4

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{x}{6}$ by $\frac{4}{4}$ .

$\frac{x \cdot 4}{6 \cdot 4} + \frac{3 x}{8} \cdot \frac{3}{3} - 3$

Step 4.2

Multiply $6$ by $4$ .

$\frac{x \cdot 4}{24} + \frac{3 x}{8} \cdot \frac{3}{3} - 3$

Step 4.3

Multiply $\frac{3 x}{8}$ by $\frac{3}{3}$ .

$\frac{x \cdot 4}{24} + \frac{3 x \cdot 3}{8 \cdot 3} - 3$

Step 4.4

Multiply $8$ by $3$ .

$\frac{x \cdot 4}{24} + \frac{3 x \cdot 3}{24} - 3$

Step 5

Combine the numerators over the common denominator.

$\frac{x \cdot 4 + 3 x \cdot 3}{24} - 3$

Step 6

Simplify each term.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

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

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Step 6.1.1.1

Factor $x$ out of $x \cdot 4$ .

$\frac{x (4) + 3 x \cdot 3}{24} - 3$

Step 6.1.1.2

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

$\frac{x (4) + x (3 \cdot 3)}{24} - 3$

Step 6.1.1.3

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

$\frac{x (4 + 3 \cdot 3)}{24} - 3$

Step 6.1.2

Multiply $3$ by $3$ .

$\frac{x (4 + 9)}{24} - 3$

Step 6.1.3

Add $4$ and $9$ .

$\frac{x \cdot 13}{24} - 3$

Step 6.2

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

$\frac{13 x}{24} - 3$