Pre-Algebra Examples

$y - 80 = - \frac{21}{4} \cdot (x - 10)$

Step 1

Rewrite the equation as $- \frac{21}{4} \cdot (x - 10) = y - 80$ .

$- \frac{21}{4} \cdot (x - 10) = y - 80$

Step 2

Multiply both sides of the equation by $- \frac{4}{21}$ .

$- \frac{4}{21} (- \frac{21}{4} \cdot (x - 10)) = - \frac{4}{21} (y - 80)$

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 $- \frac{4}{21} (- \frac{21}{4} \cdot (x - 10))$ .

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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.

$- \frac{4}{21} (- \frac{21}{4} x - \frac{21}{4} \cdot - 10) = - \frac{4}{21} (y - 80)$

Step 3.1.1.1.2

Combine $x$ and $\frac{21}{4}$ .

$- \frac{4}{21} (- \frac{x \cdot 21}{4} - \frac{21}{4} \cdot - 10) = - \frac{4}{21} (y - 80)$

Step 3.1.1.1.3

Cancel the common factor of $2$ .

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Step 3.1.1.1.3.1

Move the leading negative in $- \frac{21}{4}$ into the numerator.

$- \frac{4}{21} (- \frac{x \cdot 21}{4} + \frac{- 21}{4} \cdot - 10) = - \frac{4}{21} (y - 80)$

Step 3.1.1.1.3.2

Factor $2$ out of $4$ .

$- \frac{4}{21} (- \frac{x \cdot 21}{4} + \frac{- 21}{2 (2)} \cdot - 10) = - \frac{4}{21} (y - 80)$

Step 3.1.1.1.3.3

Factor $2$ out of $- 10$ .

$- \frac{4}{21} (- \frac{x \cdot 21}{4} + \frac{- 21}{2 \cdot 2} \cdot (2 \cdot - 5)) = - \frac{4}{21} (y - 80)$

Step 3.1.1.1.3.4

Cancel the common factor.

$- \frac{4}{21} (- \frac{x \cdot 21}{4} + \frac{- 21}{2 \cdot 2} \cdot (2 \cdot - 5)) = - \frac{4}{21} (y - 80)$

Step 3.1.1.1.3.5

Rewrite the expression.

$- \frac{4}{21} (- \frac{x \cdot 21}{4} + \frac{- 21}{2} \cdot - 5) = - \frac{4}{21} (y - 80)$

Step 3.1.1.1.4

Combine $\frac{- 21}{2}$ and $- 5$ .

$- \frac{4}{21} (- \frac{x \cdot 21}{4} + \frac{- 21 \cdot - 5}{2}) = - \frac{4}{21} (y - 80)$

Step 3.1.1.1.5

Multiply $- 21$ by $- 5$ .

$- \frac{4}{21} (- \frac{x \cdot 21}{4} + \frac{105}{2}) = - \frac{4}{21} (y - 80)$

Step 3.1.1.2

Move $21$ to the left of $x$ .

$- \frac{4}{21} (- \frac{21 x}{4} + \frac{105}{2}) = - \frac{4}{21} (y - 80)$

Step 3.1.1.3

Simplify terms.

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Step 3.1.1.3.1

Apply the distributive property.

$- \frac{4}{21} (- \frac{21 x}{4}) - \frac{4}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.2

Cancel the common factor of $4$ .

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Step 3.1.1.3.2.1

Move the leading negative in $- \frac{4}{21}$ into the numerator.

$\frac{- 4}{21} (- \frac{21 x}{4}) - \frac{4}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.2.2

Move the leading negative in $- \frac{21 x}{4}$ into the numerator.

$\frac{- 4}{21} \cdot \frac{- 21 x}{4} - \frac{4}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.2.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{21} \cdot \frac{- 21 x}{4} - \frac{4}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.2.4

Cancel the common factor.

$\frac{4 \cdot - 1}{21} \cdot \frac{- 21 x}{4} - \frac{4}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.2.5

Rewrite the expression.

$\frac{- 1}{21} (- 21 x) - \frac{4}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.3

Cancel the common factor of $21$ .

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Step 3.1.1.3.3.1

Factor $21$ out of $- 21 x$ .

$\frac{- 1}{21} (21 (- x)) - \frac{4}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.3.2

Cancel the common factor.

$\frac{- 1}{21} (21 (- x)) - \frac{4}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.3.3

Rewrite the expression.

$- - x - \frac{4}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.4

Multiply.

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Step 3.1.1.3.4.1

Multiply $- 1$ by $- 1$ .

$1 x - \frac{4}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.4.2

Multiply $x$ by $1$ .

$x - \frac{4}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.5

Cancel the common factor of $2$ .

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Step 3.1.1.3.5.1

Move the leading negative in $- \frac{4}{21}$ into the numerator.

$x + \frac{- 4}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.5.2

Factor $2$ out of $- 4$ .

$x + \frac{2 (- 2)}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.5.3

Cancel the common factor.

$x + \frac{2 \cdot - 2}{21} \cdot \frac{105}{2} = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.5.4

Rewrite the expression.

$x + \frac{- 2}{21} \cdot 105 = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.6

Cancel the common factor of $21$ .

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Step 3.1.1.3.6.1

Factor $21$ out of $105$ .

$x + \frac{- 2}{21} \cdot (21 (5)) = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.6.2

Cancel the common factor.

$x + \frac{- 2}{21} \cdot (21 \cdot 5) = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.6.3

Rewrite the expression.

$x - 2 \cdot 5 = - \frac{4}{21} (y - 80)$

Step 3.1.1.3.7

Multiply $- 2$ by $5$ .

$x - 10 = - \frac{4}{21} (y - 80)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{4}{21} (y - 80)$ .

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Step 3.2.1.1

Apply the distributive property.

$x - 10 = - \frac{4}{21} y - \frac{4}{21} \cdot - 80$

Step 3.2.1.2

Combine $y$ and $\frac{4}{21}$ .

$x - 10 = - \frac{y \cdot 4}{21} - \frac{4}{21} \cdot - 80$

Step 3.2.1.3

Multiply $- \frac{4}{21} \cdot - 80$ .

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Step 3.2.1.3.1

Multiply $- 80$ by $- 1$ .

$x - 10 = - \frac{y \cdot 4}{21} + 80 (\frac{4}{21})$

Step 3.2.1.3.2

Combine $80$ and $\frac{4}{21}$ .

$x - 10 = - \frac{y \cdot 4}{21} + \frac{80 \cdot 4}{21}$

Step 3.2.1.3.3

Multiply $80$ by $4$ .

$x - 10 = - \frac{y \cdot 4}{21} + \frac{320}{21}$

Step 3.2.1.4

Move $4$ to the left of $y$ .

$x - 10 = - \frac{4 y}{21} + \frac{320}{21}$

Step 4

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

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Step 4.1

Add $10$ to both sides of the equation.

$x = - \frac{4 y}{21} + \frac{320}{21} + 10$

Step 4.2

To write $10$ as a fraction with a common denominator, multiply by $\frac{21}{21}$ .

$x = - \frac{4 y}{21} + \frac{320}{21} + 10 \cdot \frac{21}{21}$

Step 4.3

Combine $10$ and $\frac{21}{21}$ .

$x = - \frac{4 y}{21} + \frac{320}{21} + \frac{10 \cdot 21}{21}$

Step 4.4

Combine the numerators over the common denominator.

$x = - \frac{4 y}{21} + \frac{320 + 10 \cdot 21}{21}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $10$ by $21$ .

$x = - \frac{4 y}{21} + \frac{320 + 210}{21}$

Step 4.5.2

Add $320$ and $210$ .

$x = - \frac{4 y}{21} + \frac{530}{21}$