Pre-Algebra Examples

$- 3 x - \frac{1}{3} y = 17$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Multiply both sides by $3$ .

$3 (- 3 x - \frac{1}{3} y) = 3 \cdot 17$

Step 3

Simplify the left side.

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Step 3.1

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

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Step 3.1.1

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

$3 (- 3 x - \frac{y}{3}) = 3 \cdot 17$

Step 3.1.2

Apply the distributive property.

$3 (- 3 x) + 3 (- \frac{y}{3}) = 3 \cdot 17$

Step 3.1.3

Multiply $- 3$ by $3$ .

$- 9 x + 3 (- \frac{y}{3}) = 3 \cdot 17$

Step 3.1.4

Cancel the common factor of $3$ .

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Step 3.1.4.1

Move the leading negative in $- \frac{y}{3}$ into the numerator.

$- 9 x + 3 \frac{- y}{3} = 3 \cdot 17$

Step 3.1.4.2

Cancel the common factor.

$- 9 x + 3 \frac{- y}{3} = 3 \cdot 17$

Step 3.1.4.3

Rewrite the expression.

$- 9 x - y = 3 \cdot 17$

Step 4

Simplify the right side.

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Step 4.1

Multiply $3$ by $17$ .

$- 9 x - y = 51$

Step 5

Rewrite the equation.

$51 = - 9 x - y$

Step 6

Move all terms containing variables to the left side of the equation.

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Step 6.1

Add $9 x$ to both sides of the equation.

$51 + 9 x = - y$

Step 6.2

Add $y$ to both sides of the equation.

$51 + 9 x + y = 0$

Step 6.3

Move $51$ .

$9 x + y + 51 = 0$

Step 7

Subtract $51$ from both sides of the equation.

$9 x + y = - 51$

Step 8