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- Thread starter Casio
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- #1

- Feb 29, 2012

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My misunderstanding seems to be that finding the value of 'x' in this example does not prove the inequality correct?

I must be missing something here as x = 2.5 but for some reason in this example 2x - 4 < 1 mathematically does not work?

2(2.5) - 4 < 1

Is it not a typo error?

should it not be;

2(2.5) - 4

- Feb 29, 2012

- 342

Also, note that $5/2$ is not less than itself, thus it cannot be a solution! If it doesn't belong to the solution set, it cannot satisfy the given inequality.

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- #5

Let x = 2.5 - y where y may be as small or large as we desire, as long as 0 < y.

Now, substituting this into the original inequality, we find:

2(2.5 - y) - 4 < 1

5 - 2y - 4 < 1

1 - 2y < 1

0 < 2y

0 < y

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- #6

This value is definately in the inequality, so is a strick value. The misunderstanding I think I had was in understanding that ALL values up to 2.5 can be considered, so if I said;

x = - 2, which is < 2.5, I could write;

2(- 2) - 4 < 1

- 4 - 4 < 1

I understand it know, thanks everyone.