Question

Last problem! Help for medal.

I need help with just one more inequality equation...
x^2 - x - 15 > 15

Answer 1

x<-5 or x>6

Answer 2

Would you like me to explain?

Answer 3

Yes please

Answer 4

sure

Answer 5

@_greatmath7 thanks for providing an explanation in addition to the direct answer. :)

Answer 6

Let's solve your inequality step-by-step.
x^2-x-15>15
Let's find the critical points of the inequality.
(Subtract 15 from both sides): x^2-x-15-15=15-15
You then receive:
x^2-x-30=0
(Factor left side of equation):(x+5)(x-6)=0
(Set factors equal to 0):x+5=0 and x-=0

Answer 7

thnx @UsukiDoll

Answer 8

x-6=0

Answer 9

Oh I see. Thank you very much! :)

Answer 10

o_0
\[\LARGE x^2 - x - 15 > 15\]
first we subtract 15 from both sides
\[\LARGE x^2 - x - 15-15 > 15-15\]
\[\LARGE x^2 - x - 30 > 0\]

then we have to factor. our last term is -30 and the middle term is -1
6 x -5 is the only combination that can work for this quadratic equation because
6 x -5=-30
6-5 = 1

Therefore

\[\LARGE (x-6)(x+5) > 0\]

now we solve

\[\LARGE (x-6)(x+5) > 0\]

by splitting this up into two cases


\[\LARGE (x-6) > 0\]
\[\LARGE (x+5) > 0\]

solving for an inequality is the same as solving for an equation

\[\LARGE x-6 > 0\]
\[\LARGE x-6+6 > 0+6\]
\[\LARGE x > 6\]

\[\LARGE x+5 > 0\]
\[\LARGE x+5-5 > 0-5\]
\[\LARGE x > -5\]

time to switch the inequality sign
\[\LARGE x < -5\]

Answer 11

on the number line since we have < we have an open circle