Pre-Algebra Examples

$- 3 x + \frac{1}{3} = \frac{8}{3}$

Step 1

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

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Step 1.1

Subtract $\frac{1}{3}$ from both sides of the equation.

$- 3 x = \frac{8}{3} - \frac{1}{3}$

Step 1.2

Combine the numerators over the common denominator.

$- 3 x = \frac{8 - 1}{3}$

Step 1.3

Subtract $1$ from $8$ .

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

Step 2

Divide each term in $- 3 x = \frac{7}{3}$ by $- 3$ and simplify.

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Step 2.1

Divide each term in $- 3 x = \frac{7}{3}$ by $- 3$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $x$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{7}{3} \cdot \frac{1}{- 3}$

Step 2.3.2

Move the negative in front of the fraction.

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

Step 2.3.3

Multiply $\frac{7}{3} (- \frac{1}{3})$ .

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Step 2.3.3.1

Multiply $\frac{7}{3}$ by $\frac{1}{3}$ .

$x = - \frac{7}{3 \cdot 3}$

Step 2.3.3.2

Multiply $3$ by $3$ .

$x = - \frac{7}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7}{9}$

Decimal Form:

$x = - 0.\overline{7}$