Basic Math Examples

$(z - 7) - (y + 4) = 10 y$

Step 1

Simplify $z - 7 - (y + 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$z - 7 - y - 1 \cdot 4 = 10 y$

Step 1.1.2

Multiply $- 1$ by $4$ .

$z - 7 - y - 4 = 10 y$

Step 1.2

Subtract $4$ from $- 7$ .

$z - y - 11 = 10 y$

Step 2

Move all terms containing $y$ to the left side of the equation.

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Step 2.1

Subtract $10 y$ from both sides of the equation.

$z - y - 11 - 10 y = 0$

Step 2.2

Subtract $10 y$ from $- y$ .

$z - 11 y - 11 = 0$

Step 3

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

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Step 3.1

Subtract $z$ from both sides of the equation.

$- 11 y - 11 = - z$

Step 3.2

Add $11$ to both sides of the equation.

$- 11 y = - z + 11$

Step 4

Divide each term in $- 11 y = - z + 11$ by $- 11$ and simplify.

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Step 4.1

Divide each term in $- 11 y = - z + 11$ by $- 11$ .

$\frac{- 11 y}{- 11} = \frac{- z}{- 11} + \frac{11}{- 11}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 11$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 11 y}{- 11} = \frac{- z}{- 11} + \frac{11}{- 11}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- z}{- 11} + \frac{11}{- 11}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Dividing two negative values results in a positive value.

$y = \frac{z}{11} + \frac{11}{- 11}$

Step 4.3.1.2

Divide $11$ by $- 11$ .

$y = \frac{z}{11} - 1$