Finite Math Examples

$\frac{2 x}{3} - 1 = \frac{x - 2}{2}$

Step 1

Multiply both sides by $2$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{2 x}{3} - 1) \cdot 2$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{2 x}{3} \cdot 2 - 1 \cdot 2 = \frac{x - 2}{2} \cdot 2$

Step 2.1.1.2

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

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Step 2.1.1.2.1

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

$\frac{2 x \cdot 2}{3} - 1 \cdot 2 = \frac{x - 2}{2} \cdot 2$

Step 2.1.1.2.2

Multiply $2$ by $2$ .

$\frac{4 x}{3} - 1 \cdot 2 = \frac{x - 2}{2} \cdot 2$

Step 2.1.1.3

Multiply $- 1$ by $2$ .

$\frac{4 x}{3} - 2 = \frac{x - 2}{2} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 x}{3} - 2 = \frac{x - 2}{2} \cdot 2$

Step 2.2.1.2

Rewrite the expression.

$\frac{4 x}{3} - 2 = x - 2$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$\frac{4 x}{3} - 2 - x = - 2$

Step 3.1.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4 x}{3} - x \cdot \frac{3}{3} - 2 = - 2$

Step 3.1.3

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

$\frac{4 x}{3} + \frac{- x \cdot 3}{3} - 2 = - 2$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{4 x - x \cdot 3}{3} - 2 = - 2$

Step 3.1.5

Simplify each term.

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Step 3.1.5.1

Simplify the numerator.

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Step 3.1.5.1.1

Factor $x$ out of $4 x - x \cdot 3$ .

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Step 3.1.5.1.1.1

Factor $x$ out of $4 x$ .

$\frac{x \cdot 4 - x \cdot 3}{3} - 2 = - 2$

Step 3.1.5.1.1.2

Factor $x$ out of $- x \cdot 3$ .

$\frac{x \cdot 4 + x (- 1 \cdot 3)}{3} - 2 = - 2$

Step 3.1.5.1.1.3

Factor $x$ out of $x \cdot 4 + x (- 1 \cdot 3)$ .

$\frac{x (4 - 1 \cdot 3)}{3} - 2 = - 2$

Step 3.1.5.1.2

Multiply $- 1$ by $3$ .

$\frac{x (4 - 3)}{3} - 2 = - 2$

Step 3.1.5.1.3

Subtract $3$ from $4$ .

$\frac{x \cdot 1}{3} - 2 = - 2$

Step 3.1.5.2

Multiply $x$ by $1$ .

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

Step 3.2

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

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Step 3.2.1

Add $2$ to both sides of the equation.

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

Step 3.2.2

Add $- 2$ and $2$ .

$\frac{x}{3} = 0$

Step 3.3

Set the numerator equal to zero.

$x = 0$