Solve for x -9<=-2x+3<=1

$- 9 \leq - 2 x + 3 \leq 1$

Step 1

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

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 9 - 3 \leq - 2 x \leq 1 - 3$

Subtract $3$ from $- 9$ .

$- 12 \leq - 2 x \leq 1 - 3$

Subtract $3$ from $1$ .

$- 12 \leq - 2 x \leq - 2$

Step 2

Divide each term in the inequality by $- 2$ .

$\frac{- 12}{- 2} \geq \frac{- 2 x}{- 2} \geq \frac{- 2}{- 2}$

Step 3

Divide $- 12$ by $- 2$ .

$6 \geq \frac{- 2 x}{- 2} \geq \frac{- 2}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$6 \geq \frac{- 2 x}{- 2} \geq \frac{- 2}{- 2}$

Divide $x$ by $1$ .

$6 \geq x \geq \frac{- 2}{- 2}$

Step 5

Divide $- 2$ by $- 2$ .

$6 \geq x \geq 1$

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.

$1 \leq x \leq 6$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$1 \leq x \leq 6$

Interval Notation:

$[1, 6]$

Step 8