Algebra Examples

$x + \frac{1}{2} \leq - 3$ or $x - 3 > - 2$

Step 1

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

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Step 1.1

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

$x \leq - 3 - \frac{1}{2}$ or $x - 3 > - 2$

Step 1.2

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

$x \leq - 3 \cdot \frac{2}{2} - \frac{1}{2}$ or $x - 3 > - 2$

Step 1.3

Combine $- 3$ and $\frac{2}{2}$ .

$x \leq \frac{- 3 \cdot 2}{2} - \frac{1}{2}$ or $x - 3 > - 2$

Step 1.4

Combine the numerators over the common denominator.

$x \leq \frac{- 3 \cdot 2 - 1}{2}$ or $x - 3 > - 2$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 3$ by $2$ .

$x \leq \frac{- 6 - 1}{2}$ or $x - 3 > - 2$

Step 1.5.2

Subtract $1$ from $- 6$ .

$x \leq \frac{- 7}{2}$ or $x - 3 > - 2$

Step 1.6

Move the negative in front of the fraction.

$x \leq - \frac{7}{2}$ or $x - 3 > - 2$

Step 2

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

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Step 2.1

Add $3$ to both sides of the inequality.

$x \leq - \frac{7}{2}$ or $x > - 2 + 3$

Step 2.2

Add $- 2$ and $3$ .

$x \leq - \frac{7}{2}$ or $x > 1$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \leq - \frac{7}{2} or x > 1$

Interval Notation:

$(- \infty, - \frac{7}{2}] \cup (1, \infty)$

Step 4