Algebra Examples

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

Step 1

Simplify $\frac{1}{3} \cdot (5 x - 9)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{3} \cdot (5 x - 9) = 2 (\frac{1}{3} x + 6)$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply $\frac{1}{3} (5 x)$ .

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Step 1.4.1

Combine $5$ and $\frac{1}{3}$ .

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

Step 1.4.2

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

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

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $- 9$ .

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

Step 1.5.2

Cancel the common factor.

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

Step 1.5.3

Rewrite the expression.

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

Step 2

Simplify $2 (\frac{1}{3} x + 6)$ .

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Step 2.1

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

$\frac{5 x}{3} - 3 = 2 (\frac{x}{3} + 6)$

Step 2.2

Apply the distributive property.

$\frac{5 x}{3} - 3 = 2 \frac{x}{3} + 2 \cdot 6$

Step 2.3

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

$\frac{5 x}{3} - 3 = \frac{2 x}{3} + 2 \cdot 6$

Step 2.4

Multiply $2$ by $6$ .

$\frac{5 x}{3} - 3 = \frac{2 x}{3} + 12$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $\frac{2 x}{3}$ from both sides of the equation.

$\frac{5 x}{3} - 3 - \frac{2 x}{3} = 12$

Step 3.2

Combine the numerators over the common denominator.

$- 3 + \frac{5 x - 2 x}{3} = 12$

Step 3.3

Subtract $2 x$ from $5 x$ .

$- 3 + \frac{3 x}{3} = 12$

Step 3.4

Cancel the common factor of $3$ .

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Step 3.4.1

Cancel the common factor.

$- 3 + \frac{3 x}{3} = 12$

Step 3.4.2

Divide $x$ by $1$ .

$- 3 + x = 12$

Step 4

Move all terms not containing $x$ to the right side of the equation.

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Step 4.1

Add $3$ to both sides of the equation.

$x = 12 + 3$

Step 4.2

Add $12$ and $3$ .

$x = 15$