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## anonymous 4 years ago Absolute Value Question!!!

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1. anonymous

$\left| x^2 -1 \right| \le 4$

2. Ammarah

Find the vlue of x

3. anonymous

i got x is less than or equal to root 5 / x is greater than or equal to root negative 3

4. Ammarah

Could u give me a medal first plese

5. anonymous

How do you do this question? O.o

6. Ammarah

Medal first please i onlybhelp ppl who give medals

7. anonymous

Are meant to give medals first?

8. anonymous

no u answer first then get medals -_______________-

9. Ammarah

Ok so u know absolute value is always positive right?

10. anonymous

yah

11. anonymous

The number is not necessarily positive, but the definition is the value by which the number is farthest from zero (distance). Eg 1 and -1 both are 1 unit away from zero. That is why it is represented as a positive number. Also, distance can't be represented as a negative number. (e.g. You can't be -5 km away from home.)

12. Hero

|x² - 1| ≤ 4 -4 ≤ x² - 1 ≤ 4 -4 + 1 ≤ x² ≤ 4 + 1 -3 ≤ x² ≤ 5 √3 i ≤ x ≤ √5

13. Hero

Since √3i does not represent distance, the solution should only be written as x ≤ √5

14. anonymous

what about minus root five?

15. Hero

There is no minus root 5

16. anonymous

"There is actually no such thing as a plus-or-minus square root: it is merely language used to save words. For example, the equation x²=9 has two solutions, which are x=3 and x=-3. It is tedious to say: “since x²=9, x must be 3 or -3″. As a shortcut, we say: “since x²=9, x must be ±3.” http://www.xamuel.com/plus-or-minus-square-roots/

17. Hero

|x² - 1| ≤ 4 -4 ≤ x² - 1 ≤ 4 -4 + 1 ≤ x² ≤ 4 + 1 -3 ≤ x² ≤ 5 -√5 ≤ x ≤ √5

18. Hero

That should be it

19. anonymous

|x² - 1| ≤ 4 x²≤ 4+1 x²≤5 √x²≤√5 x≤√5

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