How do you solve compound inequalities #-2x + 1 > 3# and #-2x + 1 < 9#?

1 Answer
George C.
May 10, 2015

Using the shorthand notation #3 < -2x + 1 < 9#, first subtract 1 from all parts to give: #2 < -2x < 8#.

Next, divide all parts by -2 and reverse the inequalities (since -2 is negative), to give:
#-1 > x > -4#, i.e. #-4 < x < -1#.

The truth of a multi-part inequality is preserved by the following operations:
(1) Add or subtract a given number from all parts.
(2) Multiply or divide all parts by a positive number.
(3) Multiply or divide all parts by a negative number and reverse the inequalities.

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