Algebra Examples

$(\frac{1}{4} x - 5) + (\frac{3}{16} x + 8)$

Step 1

Remove parentheses.

$\frac{1}{4} x - 5 + \frac{3}{16} x + 8$

Step 2

Simplify each term.

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Step 2.1

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

$\frac{x}{4} - 5 + \frac{3}{16} x + 8$

Step 2.2

Combine $\frac{3}{16}$ and $x$ .

$\frac{x}{4} - 5 + \frac{3 x}{16} + 8$

Step 3

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

$\frac{x}{4} \cdot \frac{4}{4} + \frac{3 x}{16} - 5 + 8$

Step 4

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$\frac{x \cdot 4}{4 \cdot 4} + \frac{3 x}{16} - 5 + 8$

Step 4.2

Multiply $4$ by $4$ .

$\frac{x \cdot 4}{16} + \frac{3 x}{16} - 5 + 8$

Step 5

Combine the numerators over the common denominator.

$\frac{x \cdot 4 + 3 x}{16} - 5 + 8$

Step 6

Add $x \cdot 4$ and $3 x$ .

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Step 6.1

Reorder $x$ and $4$ .

$\frac{4 \cdot x + 3 x}{16} - 5 + 8$

Step 6.2

Add $4 \cdot x$ and $3 x$ .

$\frac{7 \cdot x}{16} - 5 + 8$

Step 7

Add $- 5$ and $8$ .

$\frac{7 x}{16} + 3$