Pre-Algebra Examples

$2 - 3 x = 13 + \frac{1}{3} y$

Step 1

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

$2 - 3 x = 13 + \frac{y}{3}$

Step 2

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

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Step 2.1

Subtract $2$ from both sides of the equation.

$- 3 x = 13 + \frac{y}{3} - 2$

Step 2.2

Subtract $2$ from $13$ .

$- 3 x = \frac{y}{3} + 11$

Step 3

Divide each term in $- 3 x = \frac{y}{3} + 11$ by $- 3$ and simplify.

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Step 3.1

Divide each term in $- 3 x = \frac{y}{3} + 11$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{\frac{y}{3}}{- 3} + \frac{11}{- 3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{\frac{y}{3}}{- 3} + \frac{11}{- 3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{y}{3}}{- 3} + \frac{11}{- 3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{y}{3} \cdot \frac{1}{- 3} + \frac{11}{- 3}$

Step 3.3.1.2

Move the negative in front of the fraction.

$x = \frac{y}{3} (- \frac{1}{3}) + \frac{11}{- 3}$

Step 3.3.1.3

Multiply $\frac{y}{3} (- \frac{1}{3})$ .

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Step 3.3.1.3.1

Multiply $\frac{y}{3}$ by $\frac{1}{3}$ .

$x = - \frac{y}{3 \cdot 3} + \frac{11}{- 3}$

Step 3.3.1.3.2

Multiply $3$ by $3$ .

$x = - \frac{y}{9} + \frac{11}{- 3}$

Step 3.3.1.4

Move the negative in front of the fraction.

$x = - \frac{y}{9} - \frac{11}{3}$