Pre-Algebra Examples

$y - 260 = - \frac{11}{5} \cdot (x - 100)$

Step 1

Rewrite the equation as $- \frac{11}{5} \cdot (x - 100) = y - 260$ .

$- \frac{11}{5} \cdot (x - 100) = y - 260$

Step 2

Multiply both sides of the equation by $- \frac{5}{11}$ .

$- \frac{5}{11} (- \frac{11}{5} \cdot (x - 100)) = - \frac{5}{11} (y - 260)$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- \frac{5}{11} (- \frac{11}{5} \cdot (x - 100))$ .

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Step 3.1.1.1

Simplify terms.

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Step 3.1.1.1.1

Apply the distributive property.

$- \frac{5}{11} (- \frac{11}{5} x - \frac{11}{5} \cdot - 100) = - \frac{5}{11} (y - 260)$

Step 3.1.1.1.2

Combine $x$ and $\frac{11}{5}$ .

$- \frac{5}{11} (- \frac{x \cdot 11}{5} - \frac{11}{5} \cdot - 100) = - \frac{5}{11} (y - 260)$

Step 3.1.1.1.3

Cancel the common factor of $5$ .

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Step 3.1.1.1.3.1

Move the leading negative in $- \frac{11}{5}$ into the numerator.

$- \frac{5}{11} (- \frac{x \cdot 11}{5} + \frac{- 11}{5} \cdot - 100) = - \frac{5}{11} (y - 260)$

Step 3.1.1.1.3.2

Factor $5$ out of $- 100$ .

$- \frac{5}{11} (- \frac{x \cdot 11}{5} + \frac{- 11}{5} \cdot (5 (- 20))) = - \frac{5}{11} (y - 260)$

Step 3.1.1.1.3.3

Cancel the common factor.

$- \frac{5}{11} (- \frac{x \cdot 11}{5} + \frac{- 11}{5} \cdot (5 \cdot - 20)) = - \frac{5}{11} (y - 260)$

Step 3.1.1.1.3.4

Rewrite the expression.

$- \frac{5}{11} (- \frac{x \cdot 11}{5} - 11 \cdot - 20) = - \frac{5}{11} (y - 260)$

Step 3.1.1.1.4

Multiply $- 11$ by $- 20$ .

$- \frac{5}{11} (- \frac{x \cdot 11}{5} + 220) = - \frac{5}{11} (y - 260)$

Step 3.1.1.2

Move $11$ to the left of $x$ .

$- \frac{5}{11} (- \frac{11 x}{5} + 220) = - \frac{5}{11} (y - 260)$

Step 3.1.1.3

Simplify terms.

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Step 3.1.1.3.1

Apply the distributive property.

$- \frac{5}{11} (- \frac{11 x}{5}) - \frac{5}{11} \cdot 220 = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.2

Cancel the common factor of $5$ .

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Step 3.1.1.3.2.1

Move the leading negative in $- \frac{5}{11}$ into the numerator.

$\frac{- 5}{11} (- \frac{11 x}{5}) - \frac{5}{11} \cdot 220 = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.2.2

Move the leading negative in $- \frac{11 x}{5}$ into the numerator.

$\frac{- 5}{11} \cdot \frac{- 11 x}{5} - \frac{5}{11} \cdot 220 = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.2.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{11} \cdot \frac{- 11 x}{5} - \frac{5}{11} \cdot 220 = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.2.4

Cancel the common factor.

$\frac{5 \cdot - 1}{11} \cdot \frac{- 11 x}{5} - \frac{5}{11} \cdot 220 = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.2.5

Rewrite the expression.

$\frac{- 1}{11} (- 11 x) - \frac{5}{11} \cdot 220 = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.3

Cancel the common factor of $11$ .

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Step 3.1.1.3.3.1

Factor $11$ out of $- 11 x$ .

$\frac{- 1}{11} (11 (- x)) - \frac{5}{11} \cdot 220 = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.3.2

Cancel the common factor.

$\frac{- 1}{11} (11 (- x)) - \frac{5}{11} \cdot 220 = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.3.3

Rewrite the expression.

$- - x - \frac{5}{11} \cdot 220 = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.4

Multiply.

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Step 3.1.1.3.4.1

Multiply $- 1$ by $- 1$ .

$1 x - \frac{5}{11} \cdot 220 = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.4.2

Multiply $x$ by $1$ .

$x - \frac{5}{11} \cdot 220 = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.5

Cancel the common factor of $11$ .

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Step 3.1.1.3.5.1

Move the leading negative in $- \frac{5}{11}$ into the numerator.

$x + \frac{- 5}{11} \cdot 220 = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.5.2

Factor $11$ out of $220$ .

$x + \frac{- 5}{11} \cdot (11 (20)) = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.5.3

Cancel the common factor.

$x + \frac{- 5}{11} \cdot (11 \cdot 20) = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.5.4

Rewrite the expression.

$x - 5 \cdot 20 = - \frac{5}{11} (y - 260)$

Step 3.1.1.3.6

Multiply $- 5$ by $20$ .

$x - 100 = - \frac{5}{11} (y - 260)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{5}{11} (y - 260)$ .

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Step 3.2.1.1

Apply the distributive property.

$x - 100 = - \frac{5}{11} y - \frac{5}{11} \cdot - 260$

Step 3.2.1.2

Combine $y$ and $\frac{5}{11}$ .

$x - 100 = - \frac{y \cdot 5}{11} - \frac{5}{11} \cdot - 260$

Step 3.2.1.3

Multiply $- \frac{5}{11} \cdot - 260$ .

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Step 3.2.1.3.1

Multiply $- 260$ by $- 1$ .

$x - 100 = - \frac{y \cdot 5}{11} + 260 (\frac{5}{11})$

Step 3.2.1.3.2

Combine $260$ and $\frac{5}{11}$ .

$x - 100 = - \frac{y \cdot 5}{11} + \frac{260 \cdot 5}{11}$

Step 3.2.1.3.3

Multiply $260$ by $5$ .

$x - 100 = - \frac{y \cdot 5}{11} + \frac{1300}{11}$

Step 3.2.1.4

Move $5$ to the left of $y$ .

$x - 100 = - \frac{5 y}{11} + \frac{1300}{11}$

Step 4

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

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Step 4.1

Add $100$ to both sides of the equation.

$x = - \frac{5 y}{11} + \frac{1300}{11} + 100$

Step 4.2

To write $100$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$x = - \frac{5 y}{11} + \frac{1300}{11} + 100 \cdot \frac{11}{11}$

Step 4.3

Combine $100$ and $\frac{11}{11}$ .

$x = - \frac{5 y}{11} + \frac{1300}{11} + \frac{100 \cdot 11}{11}$

Step 4.4

Combine the numerators over the common denominator.

$x = - \frac{5 y}{11} + \frac{1300 + 100 \cdot 11}{11}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $100$ by $11$ .

$x = - \frac{5 y}{11} + \frac{1300 + 1100}{11}$

Step 4.5.2

Add $1300$ and $1100$ .

$x = - \frac{5 y}{11} + \frac{2400}{11}$