Algebra Examples

$\frac{3 x}{5} - 3 (x + 17)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{3 x}{5} - 3 x - 3 \cdot 17$

Step 1.2

Multiply $- 3$ by $17$ .

$\frac{3 x}{5} - 3 x - 51$

Step 2

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 x}{5} - 3 x \cdot \frac{5}{5} - 51$

Step 3

Simplify terms.

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Step 3.1

Combine $- 3 x$ and $\frac{5}{5}$ .

$\frac{3 x}{5} + \frac{- 3 x \cdot 5}{5} - 51$

Step 3.2

Combine the numerators over the common denominator.

$\frac{3 x - 3 x \cdot 5}{5} - 51$

Step 4

Simplify each term.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Factor $3 x$ out of $3 x - 3 x \cdot 5$ .

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Step 4.1.1.1

Factor $3 x$ out of $3 x$ .

$\frac{3 x (1) - 3 x \cdot 5}{5} - 51$

Step 4.1.1.2

Factor $3 x$ out of $- 3 x \cdot 5$ .

$\frac{3 x (1) + 3 x (- 1 \cdot 5)}{5} - 51$

Step 4.1.1.3

Factor $3 x$ out of $3 x (1) + 3 x (- 1 \cdot 5)$ .

$\frac{3 x (1 - 1 \cdot 5)}{5} - 51$

Step 4.1.2

Multiply $- 1$ by $5$ .

$\frac{3 x (1 - 5)}{5} - 51$

Step 4.1.3

Subtract $5$ from $1$ .

$\frac{3 x \cdot - 4}{5} - 51$

Step 4.1.4

Multiply $- 4$ by $3$ .

$\frac{- 12 x}{5} - 51$

Step 4.2

Move the negative in front of the fraction.

$- \frac{12 x}{5} - 51$