Pre-Algebra Examples

$y = \frac{2}{9 x} + 3$

Step 1

Rewrite the equation as $\frac{2}{9 x} + 3 = y$ .

$\frac{2}{9 x} + 3 = y$

Step 2

Subtract $3$ from both sides of the equation.

$\frac{2}{9 x} = y - 3$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

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

$9 x, 1, 1$

Step 3.2

The LCM of one and any expression is the expression.

$9 x$

Step 4

Multiply each term in $\frac{2}{9 x} = y - 3$ by $9 x$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{2}{9 x} = y - 3$ by $9 x$ .

$\frac{2}{9 x} (9 x) = y (9 x) - 3 (9 x)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Rewrite using the commutative property of multiplication.

$9 \frac{2}{9 x} x = y (9 x) - 3 (9 x)$

Step 4.2.2

Cancel the common factor of $9$ .

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Step 4.2.2.1

Factor $9$ out of $9 x$ .

$9 \frac{2}{9 (x)} x = y (9 x) - 3 (9 x)$

Step 4.2.2.2

Cancel the common factor.

$9 \frac{2}{9 x} x = y (9 x) - 3 (9 x)$

Step 4.2.2.3

Rewrite the expression.

$\frac{2}{x} x = y (9 x) - 3 (9 x)$

Step 4.2.3

Cancel the common factor of $x$ .

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Step 4.2.3.1

Cancel the common factor.

$\frac{2}{x} x = y (9 x) - 3 (9 x)$

Step 4.2.3.2

Rewrite the expression.

$2 = y (9 x) - 3 (9 x)$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Rewrite using the commutative property of multiplication.

$2 = 9 y x - 3 (9 x)$

Step 4.3.1.2

Multiply $9$ by $- 3$ .

$2 = 9 y x - 27 x$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $9 y x - 27 x = 2$ .

$9 y x - 27 x = 2$

Step 5.2

Factor $9 x$ out of $9 y x - 27 x$ .

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Step 5.2.1

Factor $9 x$ out of $9 y x$ .

$9 x (y) - 27 x = 2$

Step 5.2.2

Factor $9 x$ out of $- 27 x$ .

$9 x (y) + 9 x (- 3) = 2$

Step 5.2.3

Factor $9 x$ out of $9 x (y) + 9 x (- 3)$ .

$9 x (y - 3) = 2$

Step 5.3

Divide each term in $9 x (y - 3) = 2$ by $9 (y - 3)$ and simplify.

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Step 5.3.1

Divide each term in $9 x (y - 3) = 2$ by $9 (y - 3)$ .

$\frac{9 x (y - 3)}{9 (y - 3)} = \frac{2}{9 (y - 3)}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $9$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{9 x (y - 3)}{9 (y - 3)} = \frac{2}{9 (y - 3)}$

Step 5.3.2.1.2

Rewrite the expression.

$\frac{x (y - 3)}{y - 3} = \frac{2}{9 (y - 3)}$

Step 5.3.2.2

Cancel the common factor of $y - 3$ .

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Step 5.3.2.2.1

Cancel the common factor.

$\frac{x (y - 3)}{y - 3} = \frac{2}{9 (y - 3)}$

Step 5.3.2.2.2

Divide $x$ by $1$ .

$x = \frac{2}{9 (y - 3)}$