Algebra Examples

$0 \leq 3 x - 6 \leq 18$

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.

$0 + 6 \leq 3 x \leq 18 + 6$

Step 1.2

Add $0$ and $6$ .

$6 \leq 3 x \leq 18 + 6$

Step 1.3

Add $18$ and $6$ .

$6 \leq 3 x \leq 24$

Step 2

Divide each term in the inequality by $3$ .

$\frac{6}{3} \leq \frac{3 x}{3} \leq \frac{24}{3}$

Step 3

Divide $6$ by $3$ .

$2 \leq \frac{3 x}{3} \leq \frac{24}{3}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

$2 \leq \frac{3 x}{3} \leq \frac{24}{3}$

Step 4.2

Divide $x$ by $1$ .

$2 \leq x \leq \frac{24}{3}$

Step 5

Divide $24$ by $3$ .

$2 \leq x \leq 8$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$2 \leq x \leq 8$

Interval Notation:

$[2, 8]$

Step 7