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

Add $2 x$ to 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 the numerator.

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Step 2.5.1

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

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Step 2.5.1.1

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

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

Step 2.5.1.2

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

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

Step 2.5.1.3

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

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

Step 2.5.2

Add $- 2$ and $3$ .

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

Step 2.5.3

Multiply $2$ by $1$ .

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

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.

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

Step 3.2

Subtract $16$ from $20$ .

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

Step 4

Multiply both sides of the equation by $\frac{3}{2}$ .

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

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

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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

Cancel the common factor.

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

Step 5.1.1.1.2

Rewrite the expression.

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

Step 5.1.1.2

Cancel the common factor of $2$ .

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Step 5.1.1.2.1

Factor $2$ out of $2 x$ .

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

Step 5.1.1.2.2

Cancel the common factor.

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

Step 5.1.1.2.3

Rewrite the expression.

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

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{3}{2} \cdot 4$ .

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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

Factor $2$ out of $4$ .

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

Step 5.2.1.1.2

Cancel the common factor.

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

Step 5.2.1.1.3

Rewrite the expression.

$x = 3 \cdot 2$

Step 5.2.1.2

Multiply $3$ by $2$ .

$x = 6$