Solve the Inequality for x -5<=4-3x<=2

$- 5 \leq 4 - 3 x \leq 2$

Step 1

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

Subtract $4$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 - 4 \leq - 3 x \leq 2 - 4$

Subtract $4$ from $- 5$ .

$- 9 \leq - 3 x \leq 2 - 4$

Subtract $4$ from $2$ .

$- 9 \leq - 3 x \leq - 2$

Step 2

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

$\frac{- 9}{- 3} \geq \frac{- 3 x}{- 3} \geq \frac{- 2}{- 3}$

Step 3

Divide $- 9$ by $- 3$ .

$3 \geq \frac{- 3 x}{- 3} \geq \frac{- 2}{- 3}$

Step 4

Cancel the common factor of $- 3$ .

Cancel the common factor.

$3 \geq \frac{- 3 x}{- 3} \geq \frac{- 2}{- 3}$

Divide $x$ by $1$ .

$3 \geq x \geq \frac{- 2}{- 3}$

Step 5

Dividing two negative values results in a positive value.

$3 \geq x \geq \frac{2}{3}$

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.

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

Step 7

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$[\frac{2}{3}, 3]$

Step 8