Basic Math Examples

$t = \frac{1}{8} \cdot (a - y + z)$

Step 1

Rewrite the equation as $\frac{1}{8} \cdot (a - y + z) = t$ .

$\frac{1}{8} \cdot (a - y + z) = t$

Step 2

Multiply both sides of the equation by $8$ .

$8 (\frac{1}{8} \cdot (a - y + z)) = 8 t$

Step 3

Simplify the left side.

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Step 3.1

Simplify $8 (\frac{1}{8} \cdot (a - y + z))$ .

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Step 3.1.1

Apply the distributive property.

$8 (\frac{1}{8} a + \frac{1}{8} (- y) + \frac{1}{8} z) = 8 t$

Step 3.1.2

Simplify.

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Step 3.1.2.1

Combine $\frac{1}{8}$ and $a$ .

$8 (\frac{a}{8} + \frac{1}{8} (- y) + \frac{1}{8} z) = 8 t$

Step 3.1.2.2

Combine $\frac{1}{8}$ and $y$ .

$8 (\frac{a}{8} - \frac{y}{8} + \frac{1}{8} z) = 8 t$

Step 3.1.2.3

Combine $\frac{1}{8}$ and $z$ .

$8 (\frac{a}{8} - \frac{y}{8} + \frac{z}{8}) = 8 t$

Step 3.1.3

Apply the distributive property.

$8 \frac{a}{8} + 8 (- \frac{y}{8}) + 8 \frac{z}{8} = 8 t$

Step 3.1.4

Simplify.

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Step 3.1.4.1

Cancel the common factor of $8$ .

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Step 3.1.4.1.1

Cancel the common factor.

$8 \frac{a}{8} + 8 (- \frac{y}{8}) + 8 \frac{z}{8} = 8 t$

Step 3.1.4.1.2

Rewrite the expression.

$a + 8 (- \frac{y}{8}) + 8 \frac{z}{8} = 8 t$

Step 3.1.4.2

Cancel the common factor of $8$ .

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Step 3.1.4.2.1

Move the leading negative in $- \frac{y}{8}$ into the numerator.

$a + 8 \frac{- y}{8} + 8 \frac{z}{8} = 8 t$

Step 3.1.4.2.2

Cancel the common factor.

$a + 8 \frac{- y}{8} + 8 \frac{z}{8} = 8 t$

Step 3.1.4.2.3

Rewrite the expression.

$a - y + 8 \frac{z}{8} = 8 t$

Step 3.1.4.3

Cancel the common factor of $8$ .

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Step 3.1.4.3.1

Cancel the common factor.

$a - y + 8 \frac{z}{8} = 8 t$

Step 3.1.4.3.2

Rewrite the expression.

$a - y + z = 8 t$

Step 4

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

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Step 4.1

Subtract $a$ from both sides of the equation.

$- y + z = 8 t - a$

Step 4.2

Subtract $z$ from both sides of the equation.

$- y = 8 t - a - z$

Step 5

Divide each term in $- y = 8 t - a - z$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- y = 8 t - a - z$ by $- 1$ .

$\frac{- y}{- 1} = \frac{8 t}{- 1} + \frac{- a}{- 1} + \frac{- z}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{8 t}{- 1} + \frac{- a}{- 1} + \frac{- z}{- 1}$

Step 5.2.2

Divide $y$ by $1$ .

$y = \frac{8 t}{- 1} + \frac{- a}{- 1} + \frac{- z}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Move the negative one from the denominator of $\frac{8 t}{- 1}$ .

$y = - 1 \cdot (8 t) + \frac{- a}{- 1} + \frac{- z}{- 1}$

Step 5.3.1.2

Rewrite $- 1 \cdot (8 t)$ as $- (8 t)$ .

$y = - (8 t) + \frac{- a}{- 1} + \frac{- z}{- 1}$

Step 5.3.1.3

Multiply $8$ by $- 1$ .

$y = - 8 t + \frac{- a}{- 1} + \frac{- z}{- 1}$

Step 5.3.1.4

Dividing two negative values results in a positive value.

$y = - 8 t + \frac{a}{1} + \frac{- z}{- 1}$

Step 5.3.1.5

Divide $a$ by $1$ .

$y = - 8 t + a + \frac{- z}{- 1}$

Step 5.3.1.6

Dividing two negative values results in a positive value.

$y = - 8 t + a + \frac{z}{1}$

Step 5.3.1.7

Divide $z$ by $1$ .

$y = - 8 t + a + z$