Precalculus Examples

$f (x) = \frac{1}{2} x + 3 x - 7$

Step 1

Rewrite the function as an equation.

$y = \frac{1}{2} x + 3 x - 7$

Step 2

Simplify $\frac{1}{2} x + 3 x - 7$ .

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Step 2.1

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

$y = \frac{x}{2} + 3 x - 7$

Step 2.2

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{x}{2} + 3 x \cdot \frac{2}{2} - 7$

Step 2.3

Simplify terms.

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Step 2.3.1

Combine $3 x$ and $\frac{2}{2}$ .

$y = \frac{x}{2} + \frac{3 x \cdot 2}{2} - 7$

Step 2.3.2

Combine the numerators over the common denominator.

$y = \frac{x + 3 x \cdot 2}{2} - 7$

Step 2.4

Simplify each term.

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Step 2.4.1

Simplify the numerator.

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Step 2.4.1.1

Factor $x$ out of $x + 3 x \cdot 2$ .

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Step 2.4.1.1.1

Raise $x$ to the power of $1$ .

$y = \frac{x^{1} + 3 x \cdot 2}{2} - 7$

Step 2.4.1.1.2

Factor $x$ out of $x^{1}$ .

$y = \frac{x \cdot 1 + 3 x \cdot 2}{2} - 7$

Step 2.4.1.1.3

Factor $x$ out of $3 x \cdot 2$ .

$y = \frac{x \cdot 1 + x (3 \cdot 2)}{2} - 7$

Step 2.4.1.1.4

Factor $x$ out of $x \cdot 1 + x (3 \cdot 2)$ .

$y = \frac{x (1 + 3 \cdot 2)}{2} - 7$

Step 2.4.1.2

Multiply $3$ by $2$ .

$y = \frac{x (1 + 6)}{2} - 7$

Step 2.4.1.3

Add $1$ and $6$ .

$y = \frac{x \cdot 7}{2} - 7$

Step 2.4.2

Move $7$ to the left of $x$ .

$y = \frac{7 x}{2} - 7$

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