Solve for x -4<5-3x<=17

$- 4 < 5 - 3 x \leq 17$

Step 1

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

Subtract $5$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 4 - 5 < - 3 x \leq 17 - 5$

Subtract $5$ from $- 4$ .

$- 9 < - 3 x \leq 17 - 5$

Subtract $5$ from $17$ .

$- 9 < - 3 x \leq 12$

Step 2

Divide each term in the inequality by $- 3$ .

$\frac{- 9}{- 3} > \frac{- 3 x}{- 3} \geq \frac{12}{- 3}$

Step 3

Divide $- 9$ by $- 3$ .

$3 > \frac{- 3 x}{- 3} \geq \frac{12}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

$3 > \frac{- 3 x}{- 3} \geq \frac{12}{- 3}$

Divide $x$ by $1$ .

$3 > x \geq \frac{12}{- 3}$

Step 5

Divide $12$ by $- 3$ .

$3 > x \geq - 4$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 4 \leq x < 3$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq x < 3$

Interval Notation:

$[- 4, 3)$

Step 8