Algebra Examples

$- 4 \leq 2 x - 6 \leq 12$

Step 1

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

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Step 1.1

Add $6$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 4 + 6 \leq 2 x \leq 12 + 6$

Step 1.2

Add $- 4$ and $6$ .

$2 \leq 2 x \leq 12 + 6$

Step 1.3

Add $12$ and $6$ .

$2 \leq 2 x \leq 18$

Step 2

Divide each term in the inequality by $2$ .

$\frac{2}{2} \leq \frac{2 x}{2} \leq \frac{18}{2}$

Step 3

Divide $2$ by $2$ .

$1 \leq \frac{2 x}{2} \leq \frac{18}{2}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$1 \leq \frac{2 x}{2} \leq \frac{18}{2}$

Step 4.2

Divide $x$ by $1$ .

$1 \leq x \leq \frac{18}{2}$

Step 5

Divide $18$ by $2$ .

$1 \leq x \leq 9$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x \leq 9$

Interval Notation:

$[1, 9]$

Step 7