Finite Math Examples

$p = 6 x + 10 t + 2 z$

Step 1

Rewrite the equation as $6 x + 10 t + 2 z = p$ .

$6 x + 10 t + 2 z = p$

Step 2

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

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Step 2.1

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

$6 x + 2 z = p - 10 t$

Step 2.2

Subtract $2 z$ from both sides of the equation.

$6 x = p - 10 t - 2 z$

Step 3

Divide each term in $6 x = p - 10 t - 2 z$ by $6$ and simplify.

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Step 3.1

Divide each term in $6 x = p - 10 t - 2 z$ by $6$ .

$\frac{6 x}{6} = \frac{p}{6} + \frac{- 10 t}{6} + \frac{- 2 z}{6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{p}{6} + \frac{- 10 t}{6} + \frac{- 2 z}{6}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{p}{6} + \frac{- 10 t}{6} + \frac{- 2 z}{6}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $- 10$ and $6$ .

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Step 3.3.1.1.1

Factor $2$ out of $- 10 t$ .

$x = \frac{p}{6} + \frac{2 (- 5 t)}{6} + \frac{- 2 z}{6}$

Step 3.3.1.1.2

Cancel the common factors.

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Step 3.3.1.1.2.1

Factor $2$ out of $6$ .

$x = \frac{p}{6} + \frac{2 (- 5 t)}{2 (3)} + \frac{- 2 z}{6}$

Step 3.3.1.1.2.2

Cancel the common factor.

$x = \frac{p}{6} + \frac{2 (- 5 t)}{2 \cdot 3} + \frac{- 2 z}{6}$

Step 3.3.1.1.2.3

Rewrite the expression.

$x = \frac{p}{6} + \frac{- 5 t}{3} + \frac{- 2 z}{6}$

Step 3.3.1.2

Move the negative in front of the fraction.

$x = \frac{p}{6} - \frac{5 t}{3} + \frac{- 2 z}{6}$

Step 3.3.1.3

Cancel the common factor of $- 2$ and $6$ .

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Step 3.3.1.3.1

Factor $2$ out of $- 2 z$ .

$x = \frac{p}{6} - \frac{5 t}{3} + \frac{2 (- z)}{6}$

Step 3.3.1.3.2

Cancel the common factors.

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Step 3.3.1.3.2.1

Factor $2$ out of $6$ .

$x = \frac{p}{6} - \frac{5 t}{3} + \frac{2 (- z)}{2 (3)}$

Step 3.3.1.3.2.2

Cancel the common factor.

$x = \frac{p}{6} - \frac{5 t}{3} + \frac{2 (- z)}{2 \cdot 3}$

Step 3.3.1.3.2.3

Rewrite the expression.

$x = \frac{p}{6} - \frac{5 t}{3} + \frac{- z}{3}$

Step 3.3.1.4

Move the negative in front of the fraction.

$x = \frac{p}{6} - \frac{5 t}{3} - \frac{z}{3}$