Basic Math Examples

$\frac{(10 + 30) - (y - 50)}{4} = 20$

Step 1

Multiply both sides by $4$ .

$\frac{10 + 30 - (y - 50)}{4} \cdot 4 = 20 \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{10 + 30 - (y - 50)}{4} \cdot 4$ .

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Step 2.1.1.1

Simplify the numerator.

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Step 2.1.1.1.1

Apply the distributive property.

$\frac{10 + 30 - y - - 50}{4} \cdot 4 = 20 \cdot 4$

Step 2.1.1.1.2

Multiply $- 1$ by $- 50$ .

$\frac{10 + 30 - y + 50}{4} \cdot 4 = 20 \cdot 4$

Step 2.1.1.1.3

Add $10$ and $30$ .

$\frac{40 - y + 50}{4} \cdot 4 = 20 \cdot 4$

Step 2.1.1.1.4

Add $40$ and $50$ .

$\frac{- y + 90}{4} \cdot 4 = 20 \cdot 4$

Step 2.1.1.2

Cancel the common factor of $4$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{- y + 90}{4} \cdot 4 = 20 \cdot 4$

Step 2.1.1.2.2

Rewrite the expression.

$- y + 90 = 20 \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $20$ by $4$ .

$- y + 90 = 80$

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 $90$ from both sides of the equation.

$- y = 80 - 90$

Step 3.1.2

Subtract $90$ from $80$ .

$- y = - 10$

Step 3.2

Divide each term in $- y = - 10$ by $- 1$ and simplify.

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Step 3.2.1

Divide each term in $- y = - 10$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 10}{- 1}$

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.

$\frac{y}{1} = \frac{- 10}{- 1}$

Step 3.2.2.2

Divide $y$ by $1$ .

$y = \frac{- 10}{- 1}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 10$ by $- 1$ .

$y = 10$