Finite Math Examples

$- \frac{4}{3} x + 16 = 2 x + 20$

Step 1

Simplify each term.

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Step 1.1

Combine $x$ and $\frac{4}{3}$ .

$- \frac{x \cdot 4}{3} + 16 = 2 x + 20$

Step 1.2

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

$- \frac{4 x}{3} + 16 = 2 x + 20$

Step 2

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

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Step 2.1

Subtract $2 x$ from both sides of the equation.

$- \frac{4 x}{3} + 16 - 2 x = 20$

Step 2.2

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

$- \frac{4 x}{3} - 2 x \cdot \frac{3}{3} + 16 = 20$

Step 2.3

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

$- \frac{4 x}{3} + \frac{- 2 x \cdot 3}{3} + 16 = 20$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- 4 x - 2 x \cdot 3}{3} + 16 = 20$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $2 x$ out of $- 4 x - 2 x \cdot 3$ .

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Step 2.5.1.1.1

Factor $2 x$ out of $- 4 x$ .

$\frac{2 x (- 2) - 2 x \cdot 3}{3} + 16 = 20$

Step 2.5.1.1.2

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

$\frac{2 x (- 2) + 2 x (- 1 \cdot 3)}{3} + 16 = 20$

Step 2.5.1.1.3

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

$\frac{2 x (- 2 - 1 \cdot 3)}{3} + 16 = 20$

Step 2.5.1.2

Multiply $- 1$ by $3$ .

$\frac{2 x (- 2 - 3)}{3} + 16 = 20$

Step 2.5.1.3

Subtract $3$ from $- 2$ .

$\frac{2 x \cdot - 5}{3} + 16 = 20$

Step 2.5.1.4

Multiply $- 5$ by $2$ .

$\frac{- 10 x}{3} + 16 = 20$

Step 2.5.2

Move the negative in front of the fraction.

$- \frac{10 x}{3} + 16 = 20$

Step 3

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

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Step 3.1

Subtract $16$ from both sides of the equation.

$- \frac{10 x}{3} = 20 - 16$

Step 3.2

Subtract $16$ from $20$ .

$- \frac{10 x}{3} = 4$

Step 4

Multiply both sides of the equation by $- \frac{3}{10}$ .

$- \frac{3}{10} (- \frac{10 x}{3}) = - \frac{3}{10} \cdot 4$

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 $- \frac{3}{10} (- \frac{10 x}{3})$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{3}{10}$ into the numerator.

$\frac{- 3}{10} (- \frac{10 x}{3}) = - \frac{3}{10} \cdot 4$

Step 5.1.1.1.2

Move the leading negative in $- \frac{10 x}{3}$ into the numerator.

$\frac{- 3}{10} \cdot \frac{- 10 x}{3} = - \frac{3}{10} \cdot 4$

Step 5.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{10} \cdot \frac{- 10 x}{3} = - \frac{3}{10} \cdot 4$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{10} \cdot \frac{- 10 x}{3} = - \frac{3}{10} \cdot 4$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{10} (- 10 x) = - \frac{3}{10} \cdot 4$

Step 5.1.1.2

Cancel the common factor of $10$ .

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Step 5.1.1.2.1

Factor $10$ out of $- 10 x$ .

$\frac{- 1}{10} (10 (- x)) = - \frac{3}{10} \cdot 4$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{10} (10 (- x)) = - \frac{3}{10} \cdot 4$

Step 5.1.1.2.3

Rewrite the expression.

$- - x = - \frac{3}{10} \cdot 4$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{3}{10} \cdot 4$

Step 5.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{3}{10} \cdot 4$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{3}{10} \cdot 4$ .

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{3}{10}$ into the numerator.

$x = \frac{- 3}{10} \cdot 4$

Step 5.2.1.1.2

Factor $2$ out of $10$ .

$x = \frac{- 3}{2 (5)} \cdot 4$

Step 5.2.1.1.3

Factor $2$ out of $4$ .

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

Step 5.2.1.1.4

Cancel the common factor.

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

Step 5.2.1.1.5

Rewrite the expression.

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

Step 5.2.1.2

Combine $\frac{- 3}{5}$ and $2$ .

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

Step 5.2.1.3

Simplify the expression.

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Step 5.2.1.3.1

Multiply $- 3$ by $2$ .

$x = \frac{- 6}{5}$

Step 5.2.1.3.2

Move the negative in front of the fraction.

$x = - \frac{6}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{6}{5}$

Decimal Form:

$x = - 1.2$

Mixed Number Form:

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