Question

for what real numbers is the inequality x^2 < -4x + 45 true? (the answer is -9 < x < 5, but why doesn't x<-9 work?)

Answer 1

Let's try a number less than -9, say -10

So when x = -10, then...

x^2 < -4x + 45

(-10)^2 < -4(-10) + 45

100 < 40 + 45

100 < 85

which is false

Answer 2

Now let's try x = -11

x^2 < -4x + 45

(-11)^2 < -4(-11) + 45

121 < 44 + 45

121 < 89

which is also false

Answer 3

this continues as x gets smaller and smaller

Answer 4

so x < -9 doesn't work

Answer 5

thank you! i think i was plugging in -8 before T__T

Answer 6

that's ok, you were thinking x < 9 which happens to me all the time