Do by logic

Algebra Level 3

$\large |x^2 - 8x - 9| > x^2 - 8x - 9$

For how many integer values of $x$ , is the above expression valid ?

Notation: $| \cdot |$ denotes the absolute value function.

No solution exists Finitely many values Infinitely many values

1 solution

Marta Reece
Aug 9, 2017

If an absolute value of a number is larger than the number, it means the number must be negative.

Therefore $x^2-8x-9<0$

This is true for any $x$ in the interval $(-1, 9)$

So there is a finite number of integer values of $x$ for which the equation is true.

I don't get why there are finitely many solutions. Aren't there infinitely many values of x on that interval?

Peter van der Linden - 3 years, 10 months ago

It says integral values of $x$ , so the only $x$ 's that are solutions within that interval are 0, 1, 2, 3, 4, 5, 6, 7, 8.

Marta Reece - 3 years, 10 months ago

Integral doesn't say integer to me... For not native speakers I would change integral to integer. For integers it's obvious of course.

Peter van der Linden - 3 years, 10 months ago

@Peter van der Linden – I agree that the wording should be changed, to make it clear. (By the way, I am not a native speaker either, but I have had a lot of English practice.)

Marta Reece - 3 years, 10 months ago

Do by logic

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