Precalculus Examples

$x = \frac{2 p}{3} + 2 (2) p$

Step 1

Multiply $2$ by $2$ .

$x = \frac{2 p}{3} + 4 p$

Step 2

To write $4 p$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{2 p}{3} + 4 p \cdot \frac{3}{3}$

Step 3

Simplify terms.

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Step 3.1

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

$x = \frac{2 p}{3} + \frac{4 p \cdot 3}{3}$

Step 3.2

Combine the numerators over the common denominator.

$x = \frac{2 p + 4 p \cdot 3}{3}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $2 p$ out of $2 p + 4 p \cdot 3$ .

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Step 4.1.1

Factor $2 p$ out of $2 p$ .

$x = \frac{2 p (1) + 4 p \cdot 3}{3}$

Step 4.1.2

Factor $2 p$ out of $4 p \cdot 3$ .

$x = \frac{2 p (1) + 2 p (2 \cdot 3)}{3}$

Step 4.1.3

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

$x = \frac{2 p (1 + 2 \cdot 3)}{3}$

Step 4.2

Multiply $2$ by $3$ .

$x = \frac{2 p (1 + 6)}{3}$

Step 4.3

Add $1$ and $6$ .

$x = \frac{2 p \cdot 7}{3}$

Step 4.4

Multiply $7$ by $2$ .

$x = \frac{14 p}{3}$