Finite Math Examples

$t = \frac{1}{4} \cdot (x - y + z)$

Step 1

Rewrite the equation as $\frac{1}{4} \cdot (x - y + z) = t$ .

$\frac{1}{4} \cdot (x - y + z) = t$

Step 2

Multiply both sides of the equation by $4$ .

$4 (\frac{1}{4} \cdot (x - y + z)) = 4 t$

Step 3

Simplify the left side.

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Step 3.1

Simplify $4 (\frac{1}{4} \cdot (x - y + z))$ .

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Step 3.1.1

Apply the distributive property.

$4 (\frac{1}{4} x + \frac{1}{4} (- y) + \frac{1}{4} z) = 4 t$

Step 3.1.2

Simplify.

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Step 3.1.2.1

Combine $\frac{1}{4}$ and $x$ .

$4 (\frac{x}{4} + \frac{1}{4} (- y) + \frac{1}{4} z) = 4 t$

Step 3.1.2.2

Combine $\frac{1}{4}$ and $y$ .

$4 (\frac{x}{4} - \frac{y}{4} + \frac{1}{4} z) = 4 t$

Step 3.1.2.3

Combine $\frac{1}{4}$ and $z$ .

$4 (\frac{x}{4} - \frac{y}{4} + \frac{z}{4}) = 4 t$

Step 3.1.3

Apply the distributive property.

$4 \frac{x}{4} + 4 (- \frac{y}{4}) + 4 \frac{z}{4} = 4 t$

Step 3.1.4

Simplify.

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Step 3.1.4.1

Cancel the common factor of $4$ .

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Step 3.1.4.1.1

Cancel the common factor.

$4 \frac{x}{4} + 4 (- \frac{y}{4}) + 4 \frac{z}{4} = 4 t$

Step 3.1.4.1.2

Rewrite the expression.

$x + 4 (- \frac{y}{4}) + 4 \frac{z}{4} = 4 t$

Step 3.1.4.2

Cancel the common factor of $4$ .

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Step 3.1.4.2.1

Move the leading negative in $- \frac{y}{4}$ into the numerator.

$x + 4 \frac{- y}{4} + 4 \frac{z}{4} = 4 t$

Step 3.1.4.2.2

Cancel the common factor.

$x + 4 \frac{- y}{4} + 4 \frac{z}{4} = 4 t$

Step 3.1.4.2.3

Rewrite the expression.

$x - y + 4 \frac{z}{4} = 4 t$

Step 3.1.4.3

Cancel the common factor of $4$ .

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Step 3.1.4.3.1

Cancel the common factor.

$x - y + 4 \frac{z}{4} = 4 t$

Step 3.1.4.3.2

Rewrite the expression.

$x - y + z = 4 t$

Step 4

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

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Step 4.1

Subtract $x$ from both sides of the equation.

$- y + z = 4 t - x$

Step 4.2

Add $y$ to both sides of the equation.

$z = 4 t - x + y$