Algebra Examples

$2 - (- x - \frac{1}{2}) = - \frac{7}{2}$

Step 1

Simplify $2 - (- x - \frac{1}{2})$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 - - x - - \frac{1}{2} = - \frac{7}{2}$

Step 1.1.2

Multiply $- - x$ .

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Step 1.1.2.1

Multiply $- 1$ by $- 1$ .

$2 + 1 x - - \frac{1}{2} = - \frac{7}{2}$

Step 1.1.2.2

Multiply $x$ by $1$ .

$2 + x - - \frac{1}{2} = - \frac{7}{2}$

Step 1.1.3

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

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Step 1.1.3.1

Multiply $- 1$ by $- 1$ .

$2 + x + 1 (\frac{1}{2}) = - \frac{7}{2}$

Step 1.1.3.2

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

$2 + x + \frac{1}{2} = - \frac{7}{2}$

Step 1.2

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

$x + 2 \cdot \frac{2}{2} + \frac{1}{2} = - \frac{7}{2}$

Step 1.3

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

$x + \frac{2 \cdot 2}{2} + \frac{1}{2} = - \frac{7}{2}$

Step 1.4

Combine the numerators over the common denominator.

$x + \frac{2 \cdot 2 + 1}{2} = - \frac{7}{2}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $2$ by $2$ .

$x + \frac{4 + 1}{2} = - \frac{7}{2}$

Step 1.5.2

Add $4$ and $1$ .

$x + \frac{5}{2} = - \frac{7}{2}$

Step 2

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

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Step 2.1

Subtract $\frac{5}{2}$ from both sides of the equation.

$x = - \frac{7}{2} - \frac{5}{2}$

Step 2.2

Combine the numerators over the common denominator.

$x = \frac{- 7 - 5}{2}$

Step 2.3

Subtract $5$ from $- 7$ .

$x = \frac{- 12}{2}$

Step 2.4

Divide $- 12$ by $2$ .

$x = - 6$