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