Algebra Examples

$- 3 \leq 2 x - 1 \leq 9$

Step 1

Solve $- 1 \leq x \leq 5$ .

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Step 1.1

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

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Step 1.1.1

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

$- 3 + 1 \leq 2 x \leq 9 + 1$

Step 1.1.2

Add $- 3$ and $1$ .

$- 2 \leq 2 x \leq 9 + 1$

Step 1.1.3

Add $9$ and $1$ .

$- 2 \leq 2 x \leq 10$

Step 1.2

Divide each term in the inequality by $2$ .

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

Step 1.3

Divide $- 2$ by $2$ .

$- 1 \leq \frac{2 x}{2} \leq \frac{10}{2}$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Cancel the common factor.

$- 1 \leq \frac{2 x}{2} \leq \frac{10}{2}$

Step 1.4.2

Divide $x$ by $1$ .

$- 1 \leq x \leq \frac{10}{2}$

Step 1.5

Divide $10$ by $2$ .

$- 1 \leq x \leq 5$

Step 2

Use the inequality $- 1 \leq x \leq 5$ to build the set notation.

${x | - 1 \leq x \leq 5}$

Step 3