Question

How do you solve the compound inequalities `−22 > −5x − 7 >=−3`?

Answer 1

I will assume that the leading - before the 22 is a hyphen and not a minus sign. If it were a minus sign there would be no solution.

You can apply any of the following operations to all parts of such a compound inequality retaining its truth:
(1) Add or subtract a constant.
(2) Multiply or divide by a positive number.
(3) Multiply or divide by a negative number and reverse the signs.

Start by adding 7 to all parts to get:
`29 > -5x >= 4`

Divide by 5:
`29/5 > -x >= 4/5`

Multiply by -1 and reverse the signs:
`-29/5 < x <= -4/5`

Or in decimal notation:
`-5.8 < x <= -0.8`