Solve for x 1<=3x-2<16

$1 \leq 3 x - 2 < 16$

Step 1

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

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

$1 + 2 \leq 3 x < 16 + 2$

Add $1$ and $2$ .

$3 \leq 3 x < 16 + 2$

Add $16$ and $2$ .

$3 \leq 3 x < 18$

Step 2

Divide each term in the inequality by $3$ .

$\frac{3}{3} \leq \frac{3 x}{3} < \frac{18}{3}$

Step 3

Divide $3$ by $3$ .

$1 \leq \frac{3 x}{3} < \frac{18}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$1 \leq \frac{3 x}{3} < \frac{18}{3}$

Divide $x$ by $1$ .

$1 \leq x < \frac{18}{3}$

Step 5

Divide $18$ by $3$ .

$1 \leq x < 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x < 6$

Interval Notation:

$[1, 6)$

Step 7