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

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:



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



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



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

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

In all honesty, there really is no “work” per say to show. mainly it’s just using the process of elimination. the question is asking which domain(s) would be the most appropriate for the function c(n). n is the number of observed vehicles so right away, 1, 2, and 3 can be eliminated.why? 1, 2 start in the negatives and therefore it is impossible to observe negative cars. so, #4 would be the best answer to the given problem.