bettatantalo wrote:
If x² - 100 < 300, how many integers x satisfy this condition?
a) 42
b) 39
c) 38
e) 37
d) 19
Take: x² - 100 < 300
Add 100 to both sides to get: x² < 400
We know that 20² EQUALS 400, so
x must be less than 20For example,
19² < 400, so one possible solution is x =
19Likewise,
18² < 400, so another possible solution is x =
18Keep going to see that...
Another possible solution is x =
17Another possible solution is x =
16.
.
.
Another possible solution is x =
1Another possible solution is x =
0ARE WE DONE?
NO!
Negative values also work.
For example, (
-1)² = 1, and 1 < 400. So another possible solution is x =
-1And (
-2)² = 4, and 4 < 400. So another possible solution is x =
-2And (
-3)² = 9, and 9 < 400. So another possible solution is x =
-3.
.
.
And (
-19)² = 361, and 361 < 400. So another possible solution is x =
-19HOWEVER, (
-20)² = 400, and 400 is NOT less than 400.
So, the integer solutions are:
-19, -18, -17, . . . . 17, 18, 19There are 39 such solutions.
Answer: B
Cheers,
Brent
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