Algebra Examples

$2 x + \frac{1}{2} = - 5$

Step 1

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

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Step 1.1

Subtract $\frac{1}{2}$ from both sides of the equation.

$2 x = - 5 - \frac{1}{2}$

Step 1.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 x = - 5 \cdot \frac{2}{2} - \frac{1}{2}$

Step 1.3

Combine $- 5$ and $\frac{2}{2}$ .

$2 x = \frac{- 5 \cdot 2}{2} - \frac{1}{2}$

Step 1.4

Combine the numerators over the common denominator.

$2 x = \frac{- 5 \cdot 2 - 1}{2}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 5$ by $2$ .

$2 x = \frac{- 10 - 1}{2}$

Step 1.5.2

Subtract $1$ from $- 10$ .

$2 x = \frac{- 11}{2}$

Step 1.6

Move the negative in front of the fraction.

$2 x = - \frac{11}{2}$

Step 2

Divide each term in $2 x = - \frac{11}{2}$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 x = - \frac{11}{2}$ by $2$ .

$\frac{2 x}{2} = \frac{- \frac{11}{2}}{2}$

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.

$\frac{2 x}{2} = \frac{- \frac{11}{2}}{2}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{11}{2}}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{11}{2} \cdot \frac{1}{2}$

Step 2.3.2

Multiply $- \frac{11}{2} \cdot \frac{1}{2}$ .

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Step 2.3.2.1

Multiply $\frac{1}{2}$ by $\frac{11}{2}$ .

$x = - \frac{11}{2 \cdot 2}$

Step 2.3.2.2

Multiply $2$ by $2$ .

$x = - \frac{11}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{11}{4}$

Decimal Form:

$x = - 2.75$

Mixed Number Form:

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