Basic Math Examples

$\frac{8 - y}{21 - 5} = \frac{5}{4}$

Step 1

Multiply both sides by $21 - 5$ .

$\frac{8 - y}{21 - 5} (21 - 5) = \frac{5}{4} (21 - 5)$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{8 - y}{21 - 5} (21 - 5)$ .

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Step 2.1.1.1

Cancel the common factor of $21 - 5$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{8 - y}{21 - 5} (21 - 5) = \frac{5}{4} (21 - 5)$

Step 2.1.1.1.2

Rewrite the expression.

$8 - y = \frac{5}{4} (21 - 5)$

Step 2.1.1.2

Reorder $8$ and $- y$ .

$- y + 8 = \frac{5}{4} (21 - 5)$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{5}{4} (21 - 5)$ .

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Step 2.2.1.1

Subtract $5$ from $21$ .

$- y + 8 = \frac{5}{4} \cdot 16$

Step 2.2.1.2

Cancel the common factor of $4$ .

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Step 2.2.1.2.1

Factor $4$ out of $16$ .

$- y + 8 = \frac{5}{4} \cdot (4 (4))$

Step 2.2.1.2.2

Cancel the common factor.

$- y + 8 = \frac{5}{4} \cdot (4 \cdot 4)$

Step 2.2.1.2.3

Rewrite the expression.

$- y + 8 = 5 \cdot 4$

Step 2.2.1.3

Multiply $5$ by $4$ .

$- y + 8 = 20$

Step 3

Solve for $y$ .

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Step 3.1

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

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Step 3.1.1

Subtract $8$ from both sides of the equation.

$- y = 20 - 8$

Step 3.1.2

Subtract $8$ from $20$ .

$- y = 12$

Step 3.2

Divide each term in $- y = 12$ by $- 1$ and simplify.

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Step 3.2.1

Divide each term in $- y = 12$ by $- 1$ .

$\frac{- y}{- 1} = \frac{12}{- 1}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{12}{- 1}$

Step 3.2.2.2

Divide $y$ by $1$ .

$y = \frac{12}{- 1}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $12$ by $- 1$ .

$y = - 12$