Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Add $x$ and $3 x$ .

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

Step 3

Find the common denominator.

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Step 3.1

Write $1$ as a fraction with denominator $1$ .

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

Step 3.2

Multiply $\frac{1}{1}$ by $\frac{12}{12}$ .

$\frac{1}{1} \cdot \frac{12}{12} + \frac{4 x}{4} + \frac{- 2}{3} + \frac{- x}{2}$

Step 3.3

Multiply $\frac{1}{1}$ by $\frac{12}{12}$ .

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

Step 3.4

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

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

Step 3.5

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

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

Step 3.6

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

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

Step 3.7

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

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

Step 3.8

Multiply $\frac{- x}{2}$ by $\frac{6}{6}$ .

$\frac{12}{12} + \frac{4 x \cdot 3}{4 \cdot 3} + \frac{- 2 \cdot 4}{3 \cdot 4} + \frac{- x}{2} \cdot \frac{6}{6}$

Step 3.9

Multiply $\frac{- x}{2}$ by $\frac{6}{6}$ .

$\frac{12}{12} + \frac{4 x \cdot 3}{4 \cdot 3} + \frac{- 2 \cdot 4}{3 \cdot 4} + \frac{- x \cdot 6}{2 \cdot 6}$

Step 3.10

Reorder the factors of $4 \cdot 3$ .

$\frac{12}{12} + \frac{4 x \cdot 3}{3 \cdot 4} + \frac{- 2 \cdot 4}{3 \cdot 4} + \frac{- x \cdot 6}{2 \cdot 6}$

Step 3.11

Multiply $3$ by $4$ .

$\frac{12}{12} + \frac{4 x \cdot 3}{12} + \frac{- 2 \cdot 4}{3 \cdot 4} + \frac{- x \cdot 6}{2 \cdot 6}$

Step 3.12

Multiply $3$ by $4$ .

$\frac{12}{12} + \frac{4 x \cdot 3}{12} + \frac{- 2 \cdot 4}{12} + \frac{- x \cdot 6}{2 \cdot 6}$

Step 3.13

Multiply $2$ by $6$ .

$\frac{12}{12} + \frac{4 x \cdot 3}{12} + \frac{- 2 \cdot 4}{12} + \frac{- x \cdot 6}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{12 + 4 x \cdot 3 - 2 \cdot 4 - x \cdot 6}{12}$

Step 5

Simplify each term.

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Step 5.1

Multiply $3$ by $4$ .

$\frac{12 + 12 x - 2 \cdot 4 - x \cdot 6}{12}$

Step 5.2

Multiply $- 2$ by $4$ .

$\frac{12 + 12 x - 8 - x \cdot 6}{12}$

Step 5.3

Multiply $6$ by $- 1$ .

$\frac{12 + 12 x - 8 - 6 x}{12}$

Step 6

Simplify terms.

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Step 6.1

Subtract $8$ from $12$ .

$\frac{12 x + 4 - 6 x}{12}$

Step 6.2

Subtract $6 x$ from $12 x$ .

$\frac{6 x + 4}{12}$

Step 6.3

Cancel the common factor of $6 x + 4$ and $12$ .

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Step 6.3.1

Factor $2$ out of $6 x$ .

$\frac{2 (3 x) + 4}{12}$

Step 6.3.2

Factor $2$ out of $4$ .

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

Step 6.3.3

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

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

Step 6.3.4

Cancel the common factors.

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Step 6.3.4.1

Factor $2$ out of $12$ .

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

Step 6.3.4.2

Cancel the common factor.

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

Step 6.3.4.3

Rewrite the expression.

$\frac{3 x + 2}{6}$