Finite Math Examples

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

Step 1

Simplify $\frac{2 x - 1}{4} + \frac{x + 2}{3}$ .

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Step 1.1

To write $\frac{2 x - 1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.2

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

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

Step 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 1.3.1

Multiply $\frac{2 x - 1}{4}$ by $\frac{3}{3}$ .

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

Step 1.3.2

Multiply $4$ by $3$ .

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

Step 1.3.3

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

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

Step 1.3.4

Multiply $3$ by $4$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Apply the distributive property.

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

Step 1.5.2

Multiply $3$ by $2$ .

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

Step 1.5.3

Multiply $- 1$ by $3$ .

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

Step 1.5.4

Apply the distributive property.

$\frac{6 x - 3 + x \cdot 4 + 2 \cdot 4}{12} = 2$

Step 1.5.5

Move $4$ to the left of $x$ .

$\frac{6 x - 3 + 4 \cdot x + 2 \cdot 4}{12} = 2$

Step 1.5.6

Multiply $2$ by $4$ .

$\frac{6 x - 3 + 4 \cdot x + 8}{12} = 2$

Step 1.5.7

Add $6 x$ and $4 x$ .

$\frac{10 x - 3 + 8}{12} = 2$

Step 1.5.8

Add $- 3$ and $8$ .

$\frac{10 x + 5}{12} = 2$

Step 1.5.9

Factor $5$ out of $10 x + 5$ .

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Step 1.5.9.1

Factor $5$ out of $10 x$ .

$\frac{5 (2 x) + 5}{12} = 2$

Step 1.5.9.2

Factor $5$ out of $5$ .

$\frac{5 (2 x) + 5 (1)}{12} = 2$

Step 1.5.9.3

Factor $5$ out of $5 (2 x) + 5 (1)$ .

$\frac{5 (2 x + 1)}{12} = 2$

Step 2

Multiply both sides by $12$ .

$\frac{5 (2 x + 1)}{12} \cdot 12 = 2 \cdot 12$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{5 (2 x + 1)}{12} \cdot 12$ .

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Step 3.1.1.1

Cancel the common factor of $12$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{5 (2 x + 1)}{12} \cdot 12 = 2 \cdot 12$

Step 3.1.1.1.2

Rewrite the expression.

$5 (2 x + 1) = 2 \cdot 12$

Step 3.1.1.2

Apply the distributive property.

$5 (2 x) + 5 \cdot 1 = 2 \cdot 12$

Step 3.1.1.3

Multiply.

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Step 3.1.1.3.1

Multiply $2$ by $5$ .

$10 x + 5 \cdot 1 = 2 \cdot 12$

Step 3.1.1.3.2

Multiply $5$ by $1$ .

$10 x + 5 = 2 \cdot 12$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $12$ .

$10 x + 5 = 24$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $5$ from both sides of the equation.

$10 x = 24 - 5$

Step 4.1.2

Subtract $5$ from $24$ .

$10 x = 19$

Step 4.2

Divide each term in $10 x = 19$ by $10$ and simplify.

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Step 4.2.1

Divide each term in $10 x = 19$ by $10$ .

$\frac{10 x}{10} = \frac{19}{10}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $10$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{10 x}{10} = \frac{19}{10}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{19}{10}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{19}{10}$

Decimal Form:

$x = 1.9$

Mixed Number Form:

$x = 1 \frac{9}{10}$