Finite Math Examples

$\frac{18 y + 3 x}{5 x + y} = 2$

Step 1

Factor $3$ out of $18 y + 3 x$ .

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Step 1.1

Factor $3$ out of $18 y$ .

$\frac{3 (6 y) + 3 x}{5 x + y} = 2$

Step 1.2

Factor $3$ out of $3 x$ .

$\frac{3 (6 y) + 3 (x)}{5 x + y} = 2$

Step 1.3

Factor $3$ out of $3 (6 y) + 3 (x)$ .

$\frac{3 (6 y + x)}{5 x + y} = 2$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$5 x + y, 1$

Step 2.2

Remove parentheses.

$5 x + y, 1$

Step 2.3

The LCM of one and any expression is the expression.

$5 x + y$

Step 3

Multiply each term in $\frac{3 (6 y + x)}{5 x + y} = 2$ by $5 x + y$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{3 (6 y + x)}{5 x + y} = 2$ by $5 x + y$ .

$\frac{3 (6 y + x)}{5 x + y} (5 x + y) = 2 (5 x + y)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5 x + y$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 (6 y + x)}{5 x + y} (5 x + y) = 2 (5 x + y)$

Step 3.2.1.2

Rewrite the expression.

$3 (6 y + x) = 2 (5 x + y)$

Step 3.2.2

Apply the distributive property.

$3 (6 y) + 3 x = 2 (5 x + y)$

Step 3.2.3

Multiply $6$ by $3$ .

$18 y + 3 x = 2 (5 x + y)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$18 y + 3 x = 2 (5 x) + 2 y$

Step 3.3.2

Multiply $5$ by $2$ .

$18 y + 3 x = 10 x + 2 y$

Step 4

Solve the equation.

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Step 4.1

Move all terms containing $y$ to the left side of the equation.

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Step 4.1.1

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

$18 y + 3 x - 2 y = 10 x$

Step 4.1.2

Subtract $2 y$ from $18 y$ .

$3 x + 16 y = 10 x$

Step 4.2

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

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Step 4.2.1

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

$16 y = 10 x - 3 x$

Step 4.2.2

Subtract $3 x$ from $10 x$ .

$16 y = 7 x$

Step 4.3

Divide each term in $16 y = 7 x$ by $16$ and simplify.

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Step 4.3.1

Divide each term in $16 y = 7 x$ by $16$ .

$\frac{16 y}{16} = \frac{7 x}{16}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $16$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{16 y}{16} = \frac{7 x}{16}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{7 x}{16}$

Step 5

The given equation $y = \frac{7 x}{16}$ can not be written as $y = k x^{2}$ , so $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x$