Finite Math Examples

$t = \frac{1}{3} \cdot (x - y + z)$

Step 1

Rewrite the equation as $\frac{1}{3} \cdot (x - y + z) = t$ .

$\frac{1}{3} \cdot (x - y + z) = t$

Step 2

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot (x - y + z)) = 3 t$

Step 3

Simplify the left side.

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Step 3.1

Simplify $3 (\frac{1}{3} \cdot (x - y + z))$ .

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Step 3.1.1

Apply the distributive property.

$3 (\frac{1}{3} x + \frac{1}{3} (- y) + \frac{1}{3} z) = 3 t$

Step 3.1.2

Simplify.

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Step 3.1.2.1

Combine $\frac{1}{3}$ and $x$ .

$3 (\frac{x}{3} + \frac{1}{3} (- y) + \frac{1}{3} z) = 3 t$

Step 3.1.2.2

Combine $\frac{1}{3}$ and $y$ .

$3 (\frac{x}{3} - \frac{y}{3} + \frac{1}{3} z) = 3 t$

Step 3.1.2.3

Combine $\frac{1}{3}$ and $z$ .

$3 (\frac{x}{3} - \frac{y}{3} + \frac{z}{3}) = 3 t$

Step 3.1.3

Apply the distributive property.

$3 \frac{x}{3} + 3 (- \frac{y}{3}) + 3 \frac{z}{3} = 3 t$

Step 3.1.4

Simplify.

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Step 3.1.4.1

Cancel the common factor of $3$ .

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Step 3.1.4.1.1

Cancel the common factor.

$3 \frac{x}{3} + 3 (- \frac{y}{3}) + 3 \frac{z}{3} = 3 t$

Step 3.1.4.1.2

Rewrite the expression.

$x + 3 (- \frac{y}{3}) + 3 \frac{z}{3} = 3 t$

Step 3.1.4.2

Cancel the common factor of $3$ .

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Step 3.1.4.2.1

Move the leading negative in $- \frac{y}{3}$ into the numerator.

$x + 3 \frac{- y}{3} + 3 \frac{z}{3} = 3 t$

Step 3.1.4.2.2

Cancel the common factor.

$x + 3 \frac{- y}{3} + 3 \frac{z}{3} = 3 t$

Step 3.1.4.2.3

Rewrite the expression.

$x - y + 3 \frac{z}{3} = 3 t$

Step 3.1.4.3

Cancel the common factor of $3$ .

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Step 3.1.4.3.1

Cancel the common factor.

$x - y + 3 \frac{z}{3} = 3 t$

Step 3.1.4.3.2

Rewrite the expression.

$x - y + z = 3 t$

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.

$- y + z = 3 t - x$

Step 4.2

Add $y$ to both sides of the equation.

$z = 3 t - x + y$