Algebra Examples

$- 11 \leq 2 x - 1 \leq 7$

Step 1

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

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Step 1.1

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 11 + 1 \leq 2 x \leq 7 + 1$

Step 1.2

Add $- 11$ and $1$ .

$- 10 \leq 2 x \leq 7 + 1$

Step 1.3

Add $7$ and $1$ .

$- 10 \leq 2 x \leq 8$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 10}{2} \leq \frac{2 x}{2} \leq \frac{8}{2}$

Step 3

Divide $- 10$ by $2$ .

$- 5 \leq \frac{2 x}{2} \leq \frac{8}{2}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$- 5 \leq \frac{2 x}{2} \leq \frac{8}{2}$

Step 4.2

Divide $x$ by $1$ .

$- 5 \leq x \leq \frac{8}{2}$

Step 5

Divide $8$ by $2$ .

$- 5 \leq x \leq 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 5 \leq x \leq 4$

Interval Notation:

$[- 5, 4]$

Step 7