Pre-Algebra Examples

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

Step 1

Combine $\frac{1}{2}$ and $y$ .

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

Step 2

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

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

Step 3

Divide each term in $3 x = - 2 - \frac{y}{2}$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 x = - 2 - \frac{y}{2}$ by $3$ .

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

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.

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

Step 3.2.1.2

Divide $x$ by $1$ .

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

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

Move the negative in front of the fraction.

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

Step 3.3.1.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.3.1.3

Multiply $- \frac{y}{2} \cdot \frac{1}{3}$ .

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Step 3.3.1.3.1

Multiply $\frac{1}{3}$ by $\frac{y}{2}$ .

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

Step 3.3.1.3.2

Multiply $3$ by $2$ .

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