Finite Math Examples

$- \frac{x}{3} + 5 = - 2 x + 12$

Step 1

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

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Step 1.1

Add $2 x$ to both sides of the equation.

$- \frac{x}{3} + 5 + 2 x = 12$

Step 1.2

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

$- \frac{x}{3} + 2 x \cdot \frac{3}{3} + 5 = 12$

Step 1.3

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

$- \frac{x}{3} + \frac{2 x \cdot 3}{3} + 5 = 12$

Step 1.4

Combine the numerators over the common denominator.

$\frac{- x + 2 x \cdot 3}{3} + 5 = 12$

Step 1.5

Simplify each term.

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Step 1.5.1

Simplify the numerator.

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Step 1.5.1.1

Factor $x$ out of $- x + 2 x \cdot 3$ .

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Step 1.5.1.1.1

Factor $x$ out of $- x$ .

$\frac{x \cdot - 1 + 2 x \cdot 3}{3} + 5 = 12$

Step 1.5.1.1.2

Factor $x$ out of $2 x \cdot 3$ .

$\frac{x \cdot - 1 + x (2 \cdot 3)}{3} + 5 = 12$

Step 1.5.1.1.3

Factor $x$ out of $x \cdot - 1 + x (2 \cdot 3)$ .

$\frac{x (- 1 + 2 \cdot 3)}{3} + 5 = 12$

Step 1.5.1.2

Multiply $2$ by $3$ .

$\frac{x (- 1 + 6)}{3} + 5 = 12$

Step 1.5.1.3

Add $- 1$ and $6$ .

$\frac{x \cdot 5}{3} + 5 = 12$

Step 1.5.2

Move $5$ to the left of $x$ .

$\frac{5 x}{3} + 5 = 12$

Step 2

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

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Step 2.1

Subtract $5$ from both sides of the equation.

$\frac{5 x}{3} = 12 - 5$

Step 2.2

Subtract $5$ from $12$ .

$\frac{5 x}{3} = 7$

Step 3

Multiply both sides of the equation by $\frac{3}{5}$ .

$\frac{3}{5} \cdot \frac{5 x}{3} = \frac{3}{5} \cdot 7$

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 $\frac{3}{5} \cdot \frac{5 x}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{3}{5} \cdot \frac{5 x}{3} = \frac{3}{5} \cdot 7$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{3}{5} \cdot 7$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{3}{5} \cdot 7$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{3}{5} \cdot 7$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{3}{5} \cdot 7$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{3}{5} \cdot 7$ .

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Step 4.2.1.1

Combine $\frac{3}{5}$ and $7$ .

$x = \frac{3 \cdot 7}{5}$

Step 4.2.1.2

Multiply $3$ by $7$ .

$x = \frac{21}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{21}{5}$

Decimal Form:

$x = 4.2$

Mixed Number Form:

$x = 4 \frac{1}{5}$