Finite Math Examples

$9 x + \frac{3}{2} y = 11$

Step 1

Combine $\frac{3}{2}$ and $y$ .

$9 x + \frac{3 y}{2} = 11$

Step 2

Subtract $9 x$ from both sides of the equation.

$\frac{3 y}{2} = 11 - 9 x$

Step 3

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 y}{2} = \frac{2}{3} (11 - 9 x)$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{2}{3} \cdot \frac{3 y}{2}$ .

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 y}{2} = \frac{2}{3} (11 - 9 x)$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 y) = \frac{2}{3} (11 - 9 x)$

$\frac{1}{3} (3 y) = \frac{2}{3} (11 - 9 x)$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Factor $3$ out of $3 y$ .

$\frac{1}{3} (3 (y)) = \frac{2}{3} (11 - 9 x)$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 y) = \frac{2}{3} (11 - 9 x)$

Step 4.1.1.2.3

Rewrite the expression.

$y = \frac{2}{3} (11 - 9 x)$

$y = \frac{2}{3} (11 - 9 x)$

$y = \frac{2}{3} (11 - 9 x)$

$y = \frac{2}{3} (11 - 9 x)$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{2}{3} (11 - 9 x)$ .

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Step 4.2.1.1

Apply the distributive property.

$y = \frac{2}{3} \cdot 11 + \frac{2}{3} (- 9 x)$

Step 4.2.1.2

Multiply $\frac{2}{3} \cdot 11$ .

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Step 4.2.1.2.1

Combine $\frac{2}{3}$ and $11$ .

$y = \frac{2 \cdot 11}{3} + \frac{2}{3} (- 9 x)$

Step 4.2.1.2.2

Multiply $2$ by $11$ .

$y = \frac{22}{3} + \frac{2}{3} (- 9 x)$

$y = \frac{22}{3} + \frac{2}{3} (- 9 x)$

Step 4.2.1.3

Cancel the common factor of $3$ .

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Step 4.2.1.3.1

Factor $3$ out of $- 9 x$ .

$y = \frac{22}{3} + \frac{2}{3} (3 (- 3 x))$

Step 4.2.1.3.2

Cancel the common factor.

$y = \frac{22}{3} + \frac{2}{3} (3 (- 3 x))$

Step 4.2.1.3.3

Rewrite the expression.

$y = \frac{22}{3} + 2 (- 3 x)$

$y = \frac{22}{3} + 2 (- 3 x)$

Step 4.2.1.4

Multiply $- 3$ by $2$ .

$y = \frac{22}{3} - 6 x$

$y = \frac{22}{3} - 6 x$

$y = \frac{22}{3} - 6 x$

$y = \frac{22}{3} - 6 x$

Step 5

Reorder $\frac{22}{3}$ and $- 6 x$ .

$y = - 6 x + \frac{22}{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$