Pre-Algebra Examples

$\frac{1}{2} \cdot (- 4 + 6 x) = \frac{1}{3} x + \frac{2}{3} \cdot (x + 9)$

Step 1

Simplify $\frac{1}{2} \cdot (- 4 + 6 x)$ .

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Step 1.1

Apply the distributive property.

$\frac{1}{2} \cdot - 4 + \frac{1}{2} (6 x) = \frac{1}{3} x + \frac{2}{3} \cdot (x + 9)$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $- 4$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $6 x$ .

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

Step 1.3.2

Cancel the common factor.

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

Step 1.3.3

Rewrite the expression.

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

Step 2

Simplify $\frac{1}{3} x + \frac{2}{3} \cdot (x + 9)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $\frac{1}{3}$ and $x$ .

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

Step 2.1.2

Apply the distributive property.

$- 2 + 3 x = \frac{x}{3} + \frac{2}{3} x + \frac{2}{3} \cdot 9$

Step 2.1.3

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

$- 2 + 3 x = \frac{x}{3} + \frac{2 x}{3} + \frac{2}{3} \cdot 9$

Step 2.1.4

Cancel the common factor of $3$ .

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Step 2.1.4.1

Factor $3$ out of $9$ .

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

Step 2.1.4.2

Cancel the common factor.

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

Step 2.1.4.3

Rewrite the expression.

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

Step 2.1.5

Multiply $2$ by $3$ .

$- 2 + 3 x = \frac{x}{3} + \frac{2 x}{3} + 6$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the numerators over the common denominator.

$- 2 + 3 x = 6 + \frac{x + 2 x}{3}$

Step 2.2.2

Add $x$ and $2 x$ .

$- 2 + 3 x = 6 + \frac{3 x}{3}$

Step 2.2.3

Cancel the common factor of $3$ .

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Step 2.2.3.1

Cancel the common factor.

$- 2 + 3 x = 6 + \frac{3 x}{3}$

Step 2.2.3.2

Divide $x$ by $1$ .

$- 2 + 3 x = 6 + x$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 4$

Step 4