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

May 7, 2015

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:
$29 > - 5 x \ge 4$

Divide by 5:
$\frac{29}{5} > - x \ge \frac{4}{5}$

Multiply by -1 and reverse the signs:
$- \frac{29}{5} < x \le - \frac{4}{5}$

Or in decimal notation:
$- 5.8 < x \le - 0.8$