Finite Math Examples

$10 x + 5 y + 3 z = 380$

Step 1

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

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Step 1.1

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

$5 y + 3 z = 380 - 10 x$

Step 1.2

Subtract $3 z$ from both sides of the equation.

$5 y = 380 - 10 x - 3 z$

Step 2

Divide each term in $5 y = 380 - 10 x - 3 z$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 y = 380 - 10 x - 3 z$ by $5$ .

$\frac{5 y}{5} = \frac{380}{5} + \frac{- 10 x}{5} + \frac{- 3 z}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{380}{5} + \frac{- 10 x}{5} + \frac{- 3 z}{5}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{380}{5} + \frac{- 10 x}{5} + \frac{- 3 z}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $380$ by $5$ .

$y = 76 + \frac{- 10 x}{5} + \frac{- 3 z}{5}$

Step 2.3.1.2

Cancel the common factor of $- 10$ and $5$ .

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Step 2.3.1.2.1

Factor $5$ out of $- 10 x$ .

$y = 76 + \frac{5 (- 2 x)}{5} + \frac{- 3 z}{5}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $5$ out of $5$ .

$y = 76 + \frac{5 (- 2 x)}{5 (1)} + \frac{- 3 z}{5}$

Step 2.3.1.2.2.2

Cancel the common factor.

$y = 76 + \frac{5 (- 2 x)}{5 \cdot 1} + \frac{- 3 z}{5}$

Step 2.3.1.2.2.3

Rewrite the expression.

$y = 76 + \frac{- 2 x}{1} + \frac{- 3 z}{5}$

Step 2.3.1.2.2.4

Divide $- 2 x$ by $1$ .

$y = 76 - 2 x + \frac{- 3 z}{5}$

Step 2.3.1.3

Move the negative in front of the fraction.

$y = 76 - 2 x - \frac{3 z}{5}$