Algebra Examples

$x - 6 \frac{1}{2} > - 4$

Step 1

Simplify the left side.

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Step 1.1

Convert $6 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$x - (6 + \frac{1}{2}) > - 4$

Step 1.1.2

Add $6$ and $\frac{1}{2}$ .

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Step 1.1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x - (6 \cdot \frac{2}{2} + \frac{1}{2}) > - 4$

Step 1.1.2.2

Combine $6$ and $\frac{2}{2}$ .

$x - (\frac{6 \cdot 2}{2} + \frac{1}{2}) > - 4$

Step 1.1.2.3

Combine the numerators over the common denominator.

$x - \frac{6 \cdot 2 + 1}{2} > - 4$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $6$ by $2$ .

$x - \frac{12 + 1}{2} > - 4$

Step 1.1.2.4.2

Add $12$ and $1$ .

$x - \frac{13}{2} > - 4$

Step 2

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

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Step 2.1

Add $\frac{13}{2}$ to both sides of the inequality.

$x > - 4 + \frac{13}{2}$

Step 2.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x > - 4 \cdot \frac{2}{2} + \frac{13}{2}$

Step 2.3

Combine $- 4$ and $\frac{2}{2}$ .

$x > \frac{- 4 \cdot 2}{2} + \frac{13}{2}$

Step 2.4

Combine the numerators over the common denominator.

$x > \frac{- 4 \cdot 2 + 13}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 4$ by $2$ .

$x > \frac{- 8 + 13}{2}$

Step 2.5.2

Add $- 8$ and $13$ .

$x > \frac{5}{2}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{5}{2}$

Interval Notation:

$(\frac{5}{2}, \infty)$