Finite Math Examples

$33 = \frac{3}{2} x + 3$

Step 1

Rewrite the equation as $\frac{3}{2} x + 3 = 33$ .

$\frac{3}{2} x + 3 = 33$

Step 2

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

$\frac{3 x}{2} + 3 = 33$

Step 3

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

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Step 3.1

Subtract $3$ from both sides of the equation.

$\frac{3 x}{2} = 33 - 3$

Step 3.2

Subtract $3$ from $33$ .

$\frac{3 x}{2} = 30$

Step 4

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

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot 30$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

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

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} = \frac{2}{3} \cdot 30$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot 30$

Step 5.1.1.2

Cancel the common factor of $3$ .

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Step 5.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{2}{3} \cdot 30$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{2}{3} \cdot 30$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{2}{3} \cdot 30$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{2}{3} \cdot 30$ .

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Step 5.2.1.1

Cancel the common factor of $3$ .

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Step 5.2.1.1.1

Factor $3$ out of $30$ .

$x = \frac{2}{3} \cdot (3 (10))$

Step 5.2.1.1.2

Cancel the common factor.

$x = \frac{2}{3} \cdot (3 \cdot 10)$

Step 5.2.1.1.3

Rewrite the expression.

$x = 2 \cdot 10$

Step 5.2.1.2

Multiply $2$ by $10$ .

$x = 20$