Finite Math Examples

$5 x = 8 y + 1$ , $- 10 x + 16 y$

Step 1

Divide each term in $5 x = 8 y + 1$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 x = 8 y + 1$ by $5$ .

$\frac{5 x}{5} = \frac{8 y}{5} + \frac{1}{5}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{8 y}{5} + \frac{1}{5}$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{8 y}{5} + \frac{1}{5}$

Step 2

Replace the variable $x$ with $\frac{8 y}{5} + \frac{1}{5}$ in the expression.

$- 10 (\frac{8 y}{5} + \frac{1}{5}) + 16 y$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$- 10 \frac{8 y}{5} - 10 (\frac{1}{5}) + 16 y$

Step 3.2

Cancel the common factor of $5$ .

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Step 3.2.1

Factor $5$ out of $- 10$ .

$5 (- 2) \frac{8 y}{5} - 10 (\frac{1}{5}) + 16 y$

Step 3.2.2

Cancel the common factor.

$5 \cdot - 2 \frac{8 y}{5} - 10 (\frac{1}{5}) + 16 y$

Step 3.2.3

Rewrite the expression.

$- 2 (8 y) - 10 (\frac{1}{5}) + 16 y$

Step 3.3

Multiply $8$ by $- 2$ .

$- 16 y - 10 (\frac{1}{5}) + 16 y$

Step 3.4

Cancel the common factor of $5$ .

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Step 3.4.1

Factor $5$ out of $- 10$ .

$- 16 y + 5 (- 2) \frac{1}{5} + 16 y$

Step 3.4.2

Cancel the common factor.

$- 16 y + 5 \cdot - 2 \frac{1}{5} + 16 y$

Step 3.4.3

Rewrite the expression.

$- 16 y - 2 + 16 y$

Step 4

Combine the opposite terms in $- 16 y - 2 + 16 y$ .

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Step 4.1

Add $- 16 y$ and $16 y$ .

$0 - 2$

Step 4.2

Subtract $2$ from $0$ .

$- 2$