Algebra Examples

$\frac{3}{4} x - 7.3 + \frac{5}{4} x + 21.3$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{3 x}{4} - 7.3 + \frac{5}{4} x + 21.3$

Step 1.2

Combine $\frac{5}{4}$ and $x$ .

$\frac{3 x}{4} - 7.3 + \frac{5 x}{4} + 21.3$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$- 7.3 + 21.3 + \frac{3 x + 5 x}{4}$

Step 2.2

Add $3 x$ and $5 x$ .

$- 7.3 + 21.3 + \frac{8 x}{4}$

Step 3

Find the common denominator.

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Step 3.1

Write $- 7.3$ as a fraction with denominator $1$ .

$\frac{- 7.3}{1} + 21.3 + \frac{8 x}{4}$

Step 3.2

Multiply $\frac{- 7.3}{1}$ by $\frac{4}{4}$ .

$\frac{- 7.3}{1} \cdot \frac{4}{4} + 21.3 + \frac{8 x}{4}$

Step 3.3

Multiply $\frac{- 7.3}{1}$ by $\frac{4}{4}$ .

$\frac{- 7.3 \cdot 4}{4} + 21.3 + \frac{8 x}{4}$

Step 3.4

Write $21.3$ as a fraction with denominator $1$ .

$\frac{- 7.3 \cdot 4}{4} + \frac{21.3}{1} + \frac{8 x}{4}$

Step 3.5

Multiply $\frac{21.3}{1}$ by $\frac{4}{4}$ .

$\frac{- 7.3 \cdot 4}{4} + \frac{21.3}{1} \cdot \frac{4}{4} + \frac{8 x}{4}$

Step 3.6

Multiply $\frac{21.3}{1}$ by $\frac{4}{4}$ .

$\frac{- 7.3 \cdot 4}{4} + \frac{21.3 \cdot 4}{4} + \frac{8 x}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 7.3 \cdot 4 + 21.3 \cdot 4 + 8 x}{4}$

Step 5

Simplify each term.

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Step 5.1

Multiply $- 7.3$ by $4$ .

$\frac{- 29.2 + 21.3 \cdot 4 + 8 x}{4}$

Step 5.2

Multiply $21.3$ by $4$ .

$\frac{- 29.2 + 85.2 + 8 x}{4}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Add $- 29.2$ and $85.2$ .

$\frac{56 + 8 x}{4}$

Step 6.2

Cancel the common factor of $56 + 8 x$ and $4$ .

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Step 6.2.1

Factor $4$ out of $56$ .

$\frac{4 \cdot 14 + 8 x}{4}$

Step 6.2.2

Factor $4$ out of $8 x$ .

$\frac{4 \cdot 14 + 4 (2 x)}{4}$

Step 6.2.3

Factor $4$ out of $4 (14) + 4 (2 x)$ .

$\frac{4 (14 + 2 x)}{4}$

Step 6.2.4

Cancel the common factors.

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Step 6.2.4.1

Factor $4$ out of $4$ .

$\frac{4 (14 + 2 x)}{4 (1)}$

Step 6.2.4.2

Cancel the common factor.

$\frac{4 (14 + 2 x)}{4 \cdot 1}$

Step 6.2.4.3

Rewrite the expression.

$\frac{14 + 2 x}{1}$

Step 6.2.4.4

Divide $14 + 2 x$ by $1$ .

$14 + 2 x$