Pre-Algebra Examples

$- 6 x - 5 y = 15$

Step 1

Add $5 y$ to both sides of the equation.

$- 6 x = 15 + 5 y$

Step 2

Divide each term in $- 6 x = 15 + 5 y$ by $- 6$ and simplify.

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Step 2.1

Divide each term in $- 6 x = 15 + 5 y$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{15}{- 6} + \frac{5 y}{- 6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{15}{- 6} + \frac{5 y}{- 6}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{- 6} + \frac{5 y}{- 6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $15$ and $- 6$ .

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Step 2.3.1.1.1

Factor $3$ out of $15$ .

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

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $3$ out of $- 6$ .

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

Step 2.3.1.1.2.2

Cancel the common factor.

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

Step 2.3.1.1.2.3

Rewrite the expression.

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

Step 2.3.1.2

Move the negative in front of the fraction.

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

Step 2.3.1.3

Move the negative in front of the fraction.

$x = - \frac{5}{2} - \frac{5 y}{6}$