Solve for x -14<=3x-2<7

$- 14 \leq 3 x - 2 < 7$

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.

$- 14 + 2 \leq 3 x < 7 + 2$

Add $- 14$ and $2$ .

$- 12 \leq 3 x < 7 + 2$

Add $7$ and $2$ .

$- 12 \leq 3 x < 9$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 12}{3} \leq \frac{3 x}{3} < \frac{9}{3}$

Step 3

Divide $- 12$ by $3$ .

$- 4 \leq \frac{3 x}{3} < \frac{9}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 4 \leq \frac{3 x}{3} < \frac{9}{3}$

Divide $x$ by $1$ .

$- 4 \leq x < \frac{9}{3}$

Step 5

Divide $9$ by $3$ .

$- 4 \leq x < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq x < 3$

Interval Notation:

$[- 4, 3)$

Step 7