Finite Math Examples

$\frac{3 x - 2}{4} - \frac{x - 2}{3} = \frac{2 x - 1}{6}$

Step 1

Multiply both sides by $6$ .

$(\frac{3 x - 2}{4} - \frac{x - 2}{3}) \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{3 x - 2}{4} - \frac{x - 2}{3}) \cdot 6$ .

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Step 2.1.1.1

To write $\frac{3 x - 2}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{3 x - 2}{4} \cdot \frac{3}{3} - \frac{x - 2}{3}) \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.2

To write $- \frac{x - 2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{3 x - 2}{4} \cdot \frac{3}{3} - \frac{x - 2}{3} \cdot \frac{4}{4}) \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.1.3.1

Multiply $\frac{3 x - 2}{4}$ by $\frac{3}{3}$ .

$(\frac{(3 x - 2) \cdot 3}{4 \cdot 3} - \frac{x - 2}{3} \cdot \frac{4}{4}) \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.3.2

Multiply $4$ by $3$ .

$(\frac{(3 x - 2) \cdot 3}{12} - \frac{x - 2}{3} \cdot \frac{4}{4}) \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.3.3

Multiply $\frac{x - 2}{3}$ by $\frac{4}{4}$ .

$(\frac{(3 x - 2) \cdot 3}{12} - \frac{(x - 2) \cdot 4}{3 \cdot 4}) \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.3.4

Multiply $3$ by $4$ .

$(\frac{(3 x - 2) \cdot 3}{12} - \frac{(x - 2) \cdot 4}{12}) \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.4

Combine the numerators over the common denominator.

$\frac{(3 x - 2) \cdot 3 - (x - 2) \cdot 4}{12} \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.5

Simplify the numerator.

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Step 2.1.1.5.1

Apply the distributive property.

$\frac{3 x \cdot 3 - 2 \cdot 3 - (x - 2) \cdot 4}{12} \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.5.2

Multiply $3$ by $3$ .

$\frac{9 x - 2 \cdot 3 - (x - 2) \cdot 4}{12} \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.5.3

Multiply $- 2$ by $3$ .

$\frac{9 x - 6 - (x - 2) \cdot 4}{12} \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.5.4

Apply the distributive property.

$\frac{9 x - 6 + (- x - - 2) \cdot 4}{12} \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.5.5

Multiply $- 1$ by $- 2$ .

$\frac{9 x - 6 + (- x + 2) \cdot 4}{12} \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.5.6

Apply the distributive property.

$\frac{9 x - 6 - x \cdot 4 + 2 \cdot 4}{12} \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.5.7

Multiply $4$ by $- 1$ .

$\frac{9 x - 6 - 4 x + 2 \cdot 4}{12} \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.5.8

Multiply $2$ by $4$ .

$\frac{9 x - 6 - 4 x + 8}{12} \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.5.9

Subtract $4 x$ from $9 x$ .

$\frac{5 x - 6 + 8}{12} \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.5.10

Add $- 6$ and $8$ .

$\frac{5 x + 2}{12} \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.6

Cancel the common factor of $6$ .

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Step 2.1.1.6.1

Factor $6$ out of $12$ .

$\frac{5 x + 2}{6 (2)} \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{5 x + 2}{6 \cdot 2} \cdot 6 = \frac{2 x - 1}{6} \cdot 6$

Step 2.1.1.6.3

Rewrite the expression.

$\frac{5 x + 2}{2} = \frac{2 x - 1}{6} \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 x + 2}{2} = \frac{2 x - 1}{6} \cdot 6$

Step 2.2.1.2

Rewrite the expression.

$\frac{5 x + 2}{2} = 2 x - 1$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $2$ .

$\frac{5 x + 2}{2} \cdot 2 = (2 x - 1) \cdot 2$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Cancel the common factor.

$\frac{5 x + 2}{2} \cdot 2 = (2 x - 1) \cdot 2$

Step 3.2.1.1.2

Rewrite the expression.

$5 x + 2 = (2 x - 1) \cdot 2$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify $(2 x - 1) \cdot 2$ .

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Step 3.2.2.1.1

Apply the distributive property.

$5 x + 2 = 2 x \cdot 2 - 1 \cdot 2$

Step 3.2.2.1.2

Multiply.

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Step 3.2.2.1.2.1

Multiply $2$ by $2$ .

$5 x + 2 = 4 x - 1 \cdot 2$

Step 3.2.2.1.2.2

Multiply $- 1$ by $2$ .

$5 x + 2 = 4 x - 2$

Step 3.3

Solve for $x$ .

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Step 3.3.1

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

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Step 3.3.1.1

Subtract $4 x$ from both sides of the equation.

$5 x + 2 - 4 x = - 2$

Step 3.3.1.2

Subtract $4 x$ from $5 x$ .

$x + 2 = - 2$

Step 3.3.2

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

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Step 3.3.2.1

Subtract $2$ from both sides of the equation.

$x = - 2 - 2$

Step 3.3.2.2

Subtract $2$ from $- 2$ .

$x = - 4$