Solve for x 5<=3x-1<11

$5 \leq 3 x - 1 < 11$

Step 1

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

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

$5 + 1 \leq 3 x < 11 + 1$

Add $5$ and $1$ .

$6 \leq 3 x < 11 + 1$

Add $11$ and $1$ .

$6 \leq 3 x < 12$

Step 2

Divide each term in the inequality by $3$ .

$\frac{6}{3} \leq \frac{3 x}{3} < \frac{12}{3}$

Step 3

Divide $6$ by $3$ .

$2 \leq \frac{3 x}{3} < \frac{12}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$2 \leq \frac{3 x}{3} < \frac{12}{3}$

Divide $x$ by $1$ .

$2 \leq x < \frac{12}{3}$

Step 5

Divide $12$ by $3$ .

$2 \leq x < 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$2 \leq x < 4$

Interval Notation:

$[2, 4)$

Step 7