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

1 Answer
George C.
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 > -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#

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