Help on inequalities!

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1

<p>Argg... I hate inequalities.</p>

<p>|-2x + 1 | < 1</p>

<p>So the answer would be 0 < x < 1, but how does one get to that answer?!</p>

<p>-2x + 1 < 1
-1 on both sides
-2x < 0
times -1 on both sides
2x > 0
divide 2 on both sides
x > 0</p>

<p>but how does one get x is smaller then 1??? So confused and the hot weather isn't helping :(</p>

2

<p>Anyone???</p>

<p>10char</p>

3

<p>Nevermind. I solved it :)</p>

4

<p>|a|< 1 is equivalent to -1 < a < 1. So in this case, -1 < -2x + 1 < 1. Subtract 1 to get -2 < -2x < 0. Now divide by -2 (and recall that inequalities reverse direction when you divide by a negative number) to get 1 > x > 0. This is equivalent to 0 < x < 1.</p>