Solve for x. Enter your answer in interval notation using grouping symbols.
x2 + 5x

Question

Solve for x. Enter your answer in interval notation using grouping symbols.
x2 + 5x < 24

jim_thompson5910 · Answer

First get everything to the same side. So subtract 24 from both sides
$$\Large x^2 + 5x < 24$$
$$\Large x^2 + 5x-24 < 24-24$$
$$\Large x^2 + 5x-24 < 0$$

jim_thompson5910 · Answer

what does $\Large x^2 + 5x-24 $ factor to?

confusedstudenthere · Answer

I honestly have no idea. I'm so lost in this lesson

confusedstudenthere · Answer

(x+8)(x-3) ??

jim_thompson5910 · Answer

yep

jim_thompson5910 · Answer

if you solved (x+8)(x-3) = 0, what two solutions do you get?

confusedstudenthere · Answer

(8,3) ?

jim_thompson5910 · Answer

x = -8 is the solution to x+8 = 0
x = 3 is the solution to x-3 = 0

agreed?

confusedstudenthere · Answer

yes?

jim_thompson5910 · Answer

(x+8)(x-3) = 0

means

x+8 = 0 or x-3 = 0

solve each equation to get the two solutions x = -8 or x = 3

jim_thompson5910 · Answer

so what we do is draw out a number line (see attached)

jim_thompson5910 · Answer

Then we plot the two solutions (-8 and 3) on the number line

See attached

jim_thompson5910 · Answer

The red dots break up the number line into three regions

region A in blue is from -infinity to -8 (excluding -8)
region B is in green from -8 to +3 (excluding -8, excluding +3)
region C is in purple from +3 to infinity (excluding +3)

see attached

jim_thompson5910 · Answer

with me so far @ConfusedStudentHere ?

confusedstudenthere · Answer

The third diagram confused me a bit as nothing in my lesson shows that type of graph. it only shows a green colored line like where the -8 to 3 is on those graphs you posted

jim_thompson5910 · Answer

can you show me what you mean? please post a screenshot of how your lesson is showing it

confusedstudenthere · Answer

I can not as I have already moved on from this question but I still want to understand it.

jim_thompson5910 · Answer

well the third diagram is just me color coding the 3 different regions so you can tell them apart

jim_thompson5910 · Answer

anyways, can you tell me one number lies in the blue region A?

zzr0ck3r · Answer

another way to think about it (x+8)(x-3)<0 if and only if one of the two factors is negative and the other is positive case 1 x+8>0 and x-3<0 which gives x>-8 and x<3 so -80 which gives x<-8 and x>3 and this cant happen. so the answer is -8