Algebra Examples

$- 2 x + \frac{1}{3} = \frac{1}{2}$

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.

$- 2 x = \frac{1}{2} - \frac{1}{3}$

Step 1.2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 2 x = \frac{1}{2} \cdot \frac{3}{3} - \frac{1}{3}$

Step 1.3

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 2 x = \frac{1}{2} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{2}{2}$

Step 1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$- 2 x = \frac{3}{2 \cdot 3} - \frac{1}{3} \cdot \frac{2}{2}$

Step 1.4.2

Multiply $2$ by $3$ .

$- 2 x = \frac{3}{6} - \frac{1}{3} \cdot \frac{2}{2}$

Step 1.4.3

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

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

Step 1.4.4

Multiply $3$ by $2$ .

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Subtract $2$ from $3$ .

$- 2 x = \frac{1}{6}$

Step 2

Divide each term in $- 2 x = \frac{1}{6}$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 x = \frac{1}{6}$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{\frac{1}{6}}{- 2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{\frac{1}{6}}{- 2}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{1}{6}}{- 2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{1}{6} \cdot \frac{1}{- 2}$

Step 2.3.2

Move the negative in front of the fraction.

$x = \frac{1}{6} (- \frac{1}{2})$

Step 2.3.3

Multiply $\frac{1}{6} (- \frac{1}{2})$ .

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Step 2.3.3.1

Multiply $\frac{1}{6}$ by $\frac{1}{2}$ .

$x = - \frac{1}{6 \cdot 2}$

Step 2.3.3.2

Multiply $6$ by $2$ .

$x = - \frac{1}{12}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{12}$

Decimal Form:

$x = - 0.08\overline{3}$