2 < 1 - x < 6

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

2−1<−x<6−1

Subtract 1 from 2 to get 1.

1<−x<6−1

Subtract 1 from 6 to get 5.

1<−x<5

Multiply each term in the inequality by −1.

1⋅−1>−x⋅−1>5⋅−1

Multiply 1 by −1 to get −1.

−1>−x⋅−1>5⋅−1

Multiply −x by −1 to get x.

−1> x>5⋅−1

Multiply 5 by −1 to get −5.

−1> x>−5

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

−5< x<−1

Convert the inequality to set notation.

(−5,−1)

\( 2 \leq 1 - x \leq 6\\ 1\leq-x\leq5\\ -1\geq x\geq-5\\ x\in\langle-5,1\rangle \)