Pre-Algebra Examples

$\frac{1}{3} \cdot (6 x - 9) + 5 (3 - 2 x)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{1}{3} (6 x) + \frac{1}{3} \cdot - 9 + 5 (3 - 2 x)$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Factor $3$ out of $6 x$ .

$\frac{1}{3} (3 (2 x)) + \frac{1}{3} \cdot - 9 + 5 (3 - 2 x)$

Step 1.2.2

Cancel the common factor.

$\frac{1}{3} (3 (2 x)) + \frac{1}{3} \cdot - 9 + 5 (3 - 2 x)$

Step 1.2.3

Rewrite the expression.

$2 x + \frac{1}{3} \cdot - 9 + 5 (3 - 2 x)$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Factor $3$ out of $- 9$ .

$2 x + \frac{1}{3} \cdot (3 (- 3)) + 5 (3 - 2 x)$

Step 1.3.2

Cancel the common factor.

$2 x + \frac{1}{3} \cdot (3 \cdot - 3) + 5 (3 - 2 x)$

Step 1.3.3

Rewrite the expression.

$2 x - 3 + 5 (3 - 2 x)$

Step 1.4

Apply the distributive property.

$2 x - 3 + 5 \cdot 3 + 5 (- 2 x)$

Step 1.5

Multiply $5$ by $3$ .

$2 x - 3 + 15 + 5 (- 2 x)$

Step 1.6

Multiply $- 2$ by $5$ .

$2 x - 3 + 15 - 10 x$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $10 x$ from $2 x$ .

$- 8 x - 3 + 15$

Step 2.2

Add $- 3$ and $15$ .

$- 8 x + 12$