You can
put this solution on YOUR website! please help:
|-x + 3| < 5
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Learn rules for removing absolute values from
inequalities of these forms:
Rule 1:
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|EXPRESSION| < N (where N is not negative)
Write as
-N < EXPRESSION < N
then solve. [If N is negative, there is no solution,
and solution set = Ø)
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Rule 2:
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|EXPRESSION| > N (where N is not negative
Write as
EXPRESSION < -N OR EXPRESSION > N
then solve. (If N is negative, solution set is
"all real numbers".)
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You need Rule 1. I gave you Rule 2 also because you
will need it for other problems:
|-x + 3| < 5
EXPRESSION = -x + 3
-5 < -x + 3 < 5
Add -3 to all three sides:
-5 < -x + 3 < 5
-3 -3 -3
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-8 < -x < 2
Divide all three parts by -1
which reverses the inequality
symbols:
8 > x > 2
This can also be written as
2 < x < 8
Solution in interval notation is (2, 8)
Edwin
