Solve for x -3<=1-2x<=6

$- 3 \leq 1 - 2 x \leq 6$

Step 1

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

Subtract $1$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 3 - 1 \leq - 2 x \leq 6 - 1$

Subtract $1$ from $- 3$ .

$- 4 \leq - 2 x \leq 6 - 1$

Subtract $1$ from $6$ .

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

Step 2

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

$\frac{- 4}{- 2} \geq \frac{- 2 x}{- 2} \geq \frac{5}{- 2}$

Step 3

Divide $- 4$ by $- 2$ .

$2 \geq \frac{- 2 x}{- 2} \geq \frac{5}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$2 \geq \frac{- 2 x}{- 2} \geq \frac{5}{- 2}$

Divide $x$ by $1$ .

$2 \geq x \geq \frac{5}{- 2}$

Step 5

Move the negative in front of the fraction.

$2 \geq x \geq - \frac{5}{2}$

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.

$- \frac{5}{2} \leq x \leq 2$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- \frac{5}{2} \leq x \leq 2$

Interval Notation:

$[- \frac{5}{2}, 2]$

Step 8