Pre-Algebra Examples

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

Step 1

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

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

Step 2

Multiply both sides of the equation by $8$ .

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

Step 3

Simplify the left side.

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Step 3.1

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

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Step 3.1.1

Apply the distributive property.

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

Step 3.1.2

Simplify.

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Step 3.1.2.1

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

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

Step 3.1.2.2

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

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

Step 3.1.2.3

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

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

Step 3.1.3

Apply the distributive property.

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

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.

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

Step 3.1.4.1.2

Rewrite the expression.

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

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.

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

Step 3.1.4.2.2

Cancel the common factor.

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

Step 3.1.4.2.3

Rewrite the expression.

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

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.

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

Step 3.1.4.3.2

Rewrite the expression.

$x - y + z = 8 t$

Step 4

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

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Step 4.1

Add $y$ to both sides of the equation.

$x + z = 8 t + y$

Step 4.2

Subtract $z$ from both sides of the equation.

$x = 8 t + y - z$