Algebra Examples

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

Step 1

Combine $\frac{1}{2}$ and $x$ .

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

Step 2

Move all terms not containing $x$ from the center section of the inequality.

Tap for more steps...

Step 2.1

Add $5$ to each section of the inequality because it does not contain the variable we are trying to solve for.

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

Step 2.2

Add $- 2$ and $5$ .

$3 < \frac{x}{2} < 1 + 5$

Step 2.3

Multiply each term in the inequality by $2$ .

$3 \cdot 2 < \frac{x}{2} \cdot 2 < 1 \cdot 2 + 5 \cdot 2$

Step 2.4

Multiply $3$ by $2$ .

$6 < \frac{x}{2} \cdot 2 < 1 \cdot 2 + 5 \cdot 2$

Step 2.5

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.5.1

Cancel the common factor.

$6 < \frac{x}{2} \cdot 2 < 1 \cdot 2 + 5 \cdot 2$

Step 2.5.2

Rewrite the expression.

$6 < x < 1 \cdot 2 + 5 \cdot 2$

Step 2.6

Simplify each term.

Tap for more steps...

Step 2.6.1

Multiply $2$ by $1$ .

$6 < x < 2 + 5 \cdot 2$

Step 2.6.2

Multiply $5$ by $2$ .

$6 < x < 2 + 10$

Step 2.7

Add $2$ and $10$ .

$6 < x < 12$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$6 < x < 12$

Interval Notation:

$(6, 12)$

Step 4