Pre-Algebra Examples

$| - \frac{1}{2} x + \frac{5}{2} | + \frac{1}{2} = - 8$

Step 1

Move all terms not containing $| - \frac{1}{2} x + \frac{5}{2} |$ to the right side of the equation.

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Step 1.1

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

$| - \frac{1}{2} x + \frac{5}{2} | = - 8 - \frac{1}{2}$

Step 1.2

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$| - \frac{1}{2} x + \frac{5}{2} | = - 8 \cdot \frac{2}{2} - \frac{1}{2}$

Step 1.3

Combine $- 8$ and $\frac{2}{2}$ .

$| - \frac{1}{2} x + \frac{5}{2} | = \frac{- 8 \cdot 2}{2} - \frac{1}{2}$

Step 1.4

Combine the numerators over the common denominator.

$| - \frac{1}{2} x + \frac{5}{2} | = \frac{- 8 \cdot 2 - 1}{2}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 8$ by $2$ .

$| - \frac{1}{2} x + \frac{5}{2} | = \frac{- 16 - 1}{2}$

Step 1.5.2

Subtract $1$ from $- 16$ .

$| - \frac{1}{2} x + \frac{5}{2} | = \frac{- 17}{2}$

Step 1.6

Move the negative in front of the fraction.

$| - \frac{1}{2} x + \frac{5}{2} | = - \frac{17}{2}$

Step 2

There is no value of $x$ that makes the equation be true since an absolute value can never be negative.

No solution