Precalculus Examples

$- 1 \leq 3 x - 2 < 7$

Step 1

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

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Step 1.1

Add $2$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 1 + 2 \leq 3 x < 7 + 2$

Step 1.2

Add $- 1$ and $2$ .

$1 \leq 3 x < 7 + 2$

Step 1.3

Add $7$ and $2$ .

$1 \leq 3 x < 9$

Step 2

Divide each term in the inequality by $3$ .

$\frac{1}{3} \leq \frac{3 x}{3} < \frac{9}{3}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$\frac{1}{3} \leq \frac{3 x}{3} < \frac{9}{3}$

Step 3.2

Divide $x$ by $1$ .

$\frac{1}{3} \leq x < \frac{9}{3}$

Step 4

Divide $9$ by $3$ .

$\frac{1}{3} \leq x < 3$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$\frac{1}{3} \leq x < 3$

Interval Notation:

$[\frac{1}{3}, 3)$

Step 6