Question

Find the solution of the inequality for 8 11 years ago

Answer 1

not without starting with
\[0<7x-x^2-8\]

Answer 2

or better still
\[x^2-7x+8<0\]

Answer 3

further adding, on simplify the quadratic and test the solutions,

Answer 4

unfortunately this one does not factor
you have to find the zeros using the the quadratic formula

Answer 5

how do you do that??

Answer 6

if you don't know the quadratic formula you cannot

Answer 7

\[ax^2+bx+c=0\\
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 8

oh I remember that now!

Answer 9

lol

Answer 10

when you get the two zeros, since this is a parabola that opens up, it will be negative between the two and positive outside
you want negative

Answer 11

\[x^2-7x+8<0\]
\[x^2-7x<-8\]
\[x^2-7x+\left( \frac{ 7 }{ 2 } \right)^2<-8+\left( \frac{ 7 }{ 2 } \right)^2\]
\[\left( x-\frac{ 7 }{ 2 } \right)^2<\frac{ -32+49 }{ 4 }\]
\[\left| x-\frac{ 7 }{ 2 } \right|<\frac{ \sqrt{17} }{ 2 }\]
\[-\frac{ \sqrt{17} }{ 2 }<x-\frac{ 7 }{ 2 }<\frac{ \sqrt{17} }{ 2 }\]
adding 7/2 to each inequality
\[\frac{ 7-\sqrt{17} }{ 2 }<x<\frac{ 7+\sqrt{17} }{ 2 }\]