Pre-Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Divide $6$ by $3$ .

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

Step 2

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

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Step 2.1

Subtract $2$ from both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 2$ by $3$ .

$\frac{2 x}{3} = \frac{- 2 - 6}{3}$

Step 2.5.2

Subtract $6$ from $- 2$ .

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

Step 2.6

Move the negative in front of the fraction.

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

Step 3

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

$2 x = - 8$

Step 4

Divide each term in $2 x = - 8$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 x = - 8$ by $2$ .

$\frac{2 x}{2} = \frac{- 8}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 8}{2}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 8$ by $2$ .

$x = - 4$