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anonymous
 5 years ago
How do you solve 3x2<2 ? PLEASE HELP!
anonymous
 5 years ago
How do you solve 3x2<2 ? PLEASE HELP!

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shadowfiend
 5 years ago
Best ResponseYou've already chosen the best response.0So in an absolute value situation like this, what we really mean is that these must be true: \[2 < 3x2 < 2\] This is because anything between 2 and 0, when you take the absolute value of it, will be < 2. Obviously anything between 0 and 2, when you take the absolute value of it, will also be < 2. So, we can solve this by solving the two sides simultaneously. First we add two to both sides: \[0 < 3x < 4\] Then we divide both sides by 3: \[0 < x < \frac{4}{3}\] Let's check the end points. 0  2 is 2, and its absolute value is 2. Note that our interval doesn't *include* 2, but neither does the solution *include* 0, it's just the closest endpoint. Then we check \(\frac{4}{3}\)  \(3 \cdot \frac{4}{3}  2 = 4  2 = 2\). Again, we are at a proper endpoint. So the solution looks to be correct.
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