Finite Math Examples

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

Step 1

Simplify $\frac{4}{6} x - 3 x + \frac{8}{3}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Cancel the common factor of $4$ and $6$ .

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Step 1.1.1.1

Factor $2$ out of $4$ .

$\frac{2 (2)}{6} x - 3 x + \frac{8}{3} = \frac{4}{3}$

Step 1.1.1.2

Cancel the common factors.

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Step 1.1.1.2.1

Factor $2$ out of $6$ .

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

Step 1.1.1.2.2

Cancel the common factor.

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

Step 1.1.1.2.3

Rewrite the expression.

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

Step 1.1.2

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Multiply $3$ by $- 3$ .

$\frac{2 x - 9 x + 8}{3} = \frac{4}{3}$

Step 1.7

Subtract $9 x$ from $2 x$ .

$\frac{- 7 x + 8}{3} = \frac{4}{3}$

Step 1.8

Factor $- 1$ out of $- 7 x$ .

$\frac{- (7 x) + 8}{3} = \frac{4}{3}$

Step 1.9

Rewrite $8$ as $- 1 (- 8)$ .

$\frac{- (7 x) - 1 (- 8)}{3} = \frac{4}{3}$

Step 1.10

Factor $- 1$ out of $- (7 x) - 1 (- 8)$ .

$\frac{- (7 x - 8)}{3} = \frac{4}{3}$

Step 1.11

Simplify the expression.

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Step 1.11.1

Rewrite $- (7 x - 8)$ as $- 1 (7 x - 8)$ .

$\frac{- 1 (7 x - 8)}{3} = \frac{4}{3}$

Step 1.11.2

Move the negative in front of the fraction.

$- \frac{7 x - 8}{3} = \frac{4}{3}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- (7 x - 8) = 4$

Step 3

Simplify $- (7 x - 8)$ .

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Step 3.1

Apply the distributive property.

$- (7 x) - - 8 = 4$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $7$ by $- 1$ .

$- 7 x - - 8 = 4$

Step 3.2.2

Multiply $- 1$ by $- 8$ .

$- 7 x + 8 = 4$

Step 4

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

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Step 4.1

Subtract $8$ from both sides of the equation.

$- 7 x = 4 - 8$

Step 4.2

Subtract $8$ from $4$ .

$- 7 x = - 4$

Step 5

Divide each term in $- 7 x = - 4$ by $- 7$ and simplify.

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Step 5.1

Divide each term in $- 7 x = - 4$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 4}{- 7}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 7$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 4}{- 7}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{- 7}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Dividing two negative values results in a positive value.

$x = \frac{4}{7}$

Step 6