Convert to Set Notation -1<=2-x<=1

$- 1 \leq 2 - x \leq 1$

Step 1

Solve $3 \geq x \geq 1$ .

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

Subtract $2$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 1 - 2 \leq - x \leq 1 - 2$

Subtract $2$ from $- 1$ .

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

Subtract $2$ from $1$ .

$- 3 \leq - x \leq - 1$

Multiply each term in the inequality by $- 1$ .

$\frac{- 3}{- 1} \geq \frac{- x}{- 1} \geq \frac{- 1}{- 1}$

Divide $- 3$ by $- 1$ .

$3 \geq \frac{- x}{- 1} \geq \frac{- 1}{- 1}$

Dividing two negative values results in a positive value.

$3 \geq \frac{x}{1} \geq \frac{- 1}{- 1}$

Divide $x$ by $1$ .

$3 \geq x \geq \frac{- 1}{- 1}$

Divide $- 1$ by $- 1$ .

$3 \geq x \geq 1$

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

$1 \leq x \leq 3$

Step 2

Use the inequality $1 \leq x \leq 3$ to build the set notation.

${x | 1 \leq x \leq 3}$

Step 3