Solve for x -4<=3x+17<2

$- 4 \leq 3 x + 17 < 2$

Step 1

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

Subtract $17$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 4 - 17 \leq 3 x < 2 - 17$

Subtract $17$ from $- 4$ .

$- 21 \leq 3 x < 2 - 17$

Subtract $17$ from $2$ .

$- 21 \leq 3 x < - 15$

Step 2

Divide each term in the inequality by $3$ .

$\frac{- 21}{3} \leq \frac{3 x}{3} < \frac{- 15}{3}$

Step 3

Divide $- 21$ by $3$ .

$- 7 \leq \frac{3 x}{3} < \frac{- 15}{3}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$- 7 \leq \frac{3 x}{3} < \frac{- 15}{3}$

Divide $x$ by $1$ .

$- 7 \leq x < \frac{- 15}{3}$

Step 5

Divide $- 15$ by $3$ .

$- 7 \leq x < - 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 7 \leq x < - 5$

Interval Notation:

$[- 7, - 5)$

Step 7