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Sati [7]
2 years ago
9

Which of the following is the solution to | x -12 | < 15

Mathematics
1 answer:
KiRa [710]2 years ago
7 0
Hello,
Answer D    -3<x<27
Indeed:
1)
if x-12≥0 then x≥12 and
|x-12|=x-12x-12<15 → x<27
so 12≤x<27
2) if x-12<0 then
x<12 and|x-12|=-(x-12)<15
-x+12<15-x<3 → x>-3
So -3<x<12
Thus -3<x<12  U 12≤x<27 ⇔ -3<x<27

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Now we cad divide f(x) by (x-2) which will give us a quadratic expression, which we can factorize easily (if the discriminant is non negative).

We can also try some other factors of 36. Indeed we can check that 

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Thus, the x-intercepts are (2, 0), (3, 0), (6, 0), or 2, 3, 6. 

The y-intercept is f(0), which is -36.


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and it goes to minus infinity as x goes to - infinity.
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