Algebra Examples

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

Step 1

Simplify $\frac{4}{6} x - 2 x + \frac{8}{3}$ .

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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 $4$ .

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

Step 1.1.1.2

Cancel the common factors.

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Step 1.1.1.2.1

Factor $2$ out of $6$ .

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

Step 1.1.1.2.2

Cancel the common factor.

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

Step 1.1.1.2.3

Rewrite the expression.

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

Step 1.1.2

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Multiply $3$ by $- 2$ .

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

Step 1.7

Subtract $6 x$ from $2 x$ .

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

Step 1.8

Factor $4$ out of $- 4 x + 8$ .

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Step 1.8.1

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

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

Step 1.8.2

Factor $4$ out of $8$ .

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

Step 1.8.3

Factor $4$ out of $4 (- x) + 4 (2)$ .

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

Step 1.9

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

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

Step 1.10

Rewrite $2$ as $- 1 (- 2)$ .

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

Step 1.11

Factor $- 1$ out of $- (x) - 1 (- 2)$ .

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

Step 1.12

Simplify the expression.

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Step 1.12.1

Rewrite $- (x - 2)$ as $- 1 (x - 2)$ .

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

Step 1.12.2

Move the negative in front of the fraction.

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

Step 2

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

$- 4 (x - 2) = 4$

Step 3

Divide each term in $- 4 (x - 2) = 4$ by $- 4$ and simplify.

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Step 3.1

Divide each term in $- 4 (x - 2) = 4$ by $- 4$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 4$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $x - 2$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $4$ by $- 4$ .

$x - 2 = - 1$

Step 4

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

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Step 4.1

Add $2$ to both sides of the equation.

$x = - 1 + 2$

Step 4.2

Add $- 1$ and $2$ .

$x = 1$