Algebra Examples

$- 3 y + \frac{1}{2} x = - 6$

Step 1

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

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

Step 2

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

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

Step 3

Divide each term in $- 3 y = - 6 - \frac{x}{2}$ by $- 3$ and simplify.

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Step 3.1

Divide each term in $- 3 y = - 6 - \frac{x}{2}$ by $- 3$ .

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

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.

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

Step 3.2.1.2

Divide $y$ by $1$ .

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

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

Divide $- 6$ by $- 3$ .

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

Step 3.3.1.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.3.1.3

Move the negative in front of the fraction.

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

Step 3.3.1.4

Multiply $- \frac{x}{2} (- \frac{1}{3})$ .

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Step 3.3.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 3.3.1.4.2

Multiply $\frac{x}{2}$ by $1$ .

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

Step 3.3.1.4.3

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

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

Step 3.3.1.4.4

Multiply $2$ by $3$ .

$y = 2 + \frac{x}{6}$