Algebra Examples

$\frac{1}{4} x - \frac{4}{3} + \frac{7}{2} x + \frac{5}{6}$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} - \frac{4}{3} + \frac{7}{2} x + \frac{5}{6}$

Step 1.2

Combine $\frac{7}{2}$ and $x$ .

$\frac{x}{4} - \frac{4}{3} + \frac{7 x}{2} + \frac{5}{6}$

Step 2

To write $\frac{7 x}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{4} + \frac{7 x}{2} \cdot \frac{2}{2} - \frac{4}{3} + \frac{5}{6}$

Step 3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{7 x}{2}$ by $\frac{2}{2}$ .

$\frac{x}{4} + \frac{7 x \cdot 2}{2 \cdot 2} - \frac{4}{3} + \frac{5}{6}$

Step 3.2

Multiply $2$ by $2$ .

$\frac{x}{4} + \frac{7 x \cdot 2}{4} - \frac{4}{3} + \frac{5}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{x + 7 x \cdot 2}{4} - \frac{4}{3} + \frac{5}{6}$

Step 5

Find the common denominator.

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Step 5.1

Multiply $\frac{x + 7 x \cdot 2}{4}$ by $\frac{3}{3}$ .

$\frac{x + 7 x \cdot 2}{4} \cdot \frac{3}{3} - \frac{4}{3} + \frac{5}{6}$

Step 5.2

Multiply $\frac{x + 7 x \cdot 2}{4}$ by $\frac{3}{3}$ .

$\frac{(x + 7 x \cdot 2) \cdot 3}{4 \cdot 3} - \frac{4}{3} + \frac{5}{6}$

Step 5.3

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

$\frac{(x + 7 x \cdot 2) \cdot 3}{4 \cdot 3} - (\frac{4}{3} \cdot \frac{4}{4}) + \frac{5}{6}$

Step 5.4

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

$\frac{(x + 7 x \cdot 2) \cdot 3}{4 \cdot 3} - \frac{4 \cdot 4}{3 \cdot 4} + \frac{5}{6}$

Step 5.5

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{(x + 7 x \cdot 2) \cdot 3}{4 \cdot 3} - \frac{4 \cdot 4}{3 \cdot 4} + \frac{5}{6} \cdot \frac{2}{2}$

Step 5.6

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{(x + 7 x \cdot 2) \cdot 3}{4 \cdot 3} - \frac{4 \cdot 4}{3 \cdot 4} + \frac{5 \cdot 2}{6 \cdot 2}$

Step 5.7

Reorder the factors of $4 \cdot 3$ .

$\frac{(x + 7 x \cdot 2) \cdot 3}{3 \cdot 4} - \frac{4 \cdot 4}{3 \cdot 4} + \frac{5 \cdot 2}{6 \cdot 2}$

Step 5.8

Multiply $3$ by $4$ .

$\frac{(x + 7 x \cdot 2) \cdot 3}{12} - \frac{4 \cdot 4}{3 \cdot 4} + \frac{5 \cdot 2}{6 \cdot 2}$

Step 5.9

Multiply $3$ by $4$ .

$\frac{(x + 7 x \cdot 2) \cdot 3}{12} - \frac{4 \cdot 4}{12} + \frac{5 \cdot 2}{6 \cdot 2}$

Step 5.10

Reorder the factors of $6 \cdot 2$ .

$\frac{(x + 7 x \cdot 2) \cdot 3}{12} - \frac{4 \cdot 4}{12} + \frac{5 \cdot 2}{2 \cdot 6}$

Step 5.11

Multiply $2$ by $6$ .

$\frac{(x + 7 x \cdot 2) \cdot 3}{12} - \frac{4 \cdot 4}{12} + \frac{5 \cdot 2}{12}$

Step 6

Combine the numerators over the common denominator.

$\frac{(x + 7 x \cdot 2) \cdot 3 - 4 \cdot 4 + 5 \cdot 2}{12}$

Step 7

Simplify each term.

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Step 7.1

Multiply $2$ by $7$ .

$\frac{(x + 14 x) \cdot 3 - 4 \cdot 4 + 5 \cdot 2}{12}$

Step 7.2

Add $x$ and $14 x$ .

$\frac{15 x \cdot 3 - 4 \cdot 4 + 5 \cdot 2}{12}$

Step 7.3

Multiply $3$ by $15$ .

$\frac{45 x - 4 \cdot 4 + 5 \cdot 2}{12}$

Step 7.4

Multiply $- 4$ by $4$ .

$\frac{45 x - 16 + 5 \cdot 2}{12}$

Step 7.5

Multiply $5$ by $2$ .

$\frac{45 x - 16 + 10}{12}$

Step 8

Reduce the expression by cancelling the common factors.

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Step 8.1

Add $- 16$ and $10$ .

$\frac{45 x - 6}{12}$

Step 8.2

Cancel the common factor of $45 x - 6$ and $12$ .

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Step 8.2.1

Factor $3$ out of $45 x$ .

$\frac{3 (15 x) - 6}{12}$

Step 8.2.2

Factor $3$ out of $- 6$ .

$\frac{3 (15 x) + 3 (- 2)}{12}$

Step 8.2.3

Factor $3$ out of $3 (15 x) + 3 (- 2)$ .

$\frac{3 (15 x - 2)}{12}$

Step 8.2.4

Cancel the common factors.

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Step 8.2.4.1

Factor $3$ out of $12$ .

$\frac{3 (15 x - 2)}{3 (4)}$

Step 8.2.4.2

Cancel the common factor.

$\frac{3 (15 x - 2)}{3 \cdot 4}$

Step 8.2.4.3

Rewrite the expression.

$\frac{15 x - 2}{4}$