Question

What's the solution set for the inequality x^2-2x<8?

Answer 1

$x^2-2x$

So, the numbers to base your solution set on are -2 and 4 (the numbers that the equation equal to 0)

Then, you plug in 3 numbers to the equation: a number less than -2, a number between -2 and 4, and a number greater than 4.  They represent the three sections of the number line created by the points -2 and 4.  So, our numbers will be -3, 0, and 5:

$(x-4)(x+2)$

7<0 is incorrect, so the section of the number line less than -2 does not work.

$(x-4)(x+2)$

-8<0 is correct, so the section of the number line between -2 and 4 works.

$(x-4)(x+2)$

7<0 is incorrect, so the section of the number line above 4 does not work.

So, only the section between -2 and 4 works.  However, the problem is a "less than" problem, not a "less than or equal to" problem, so -2 and 4 are not included in the solution set.  That gives you the answer:

(-2, 4)          (NOT BRACKETS because -2 and 4 are not included)