Answer:
Step-by-step explanation:
1 Factor {x}^{2}-5x+6x
2
−5x+6.
(x-3)(x-2)<0
(x−3)(x−2)<0
2 Solve for xx.
x=3,2
x=3,2
3 From the values of xx above, we have these 3 intervals to test.
\begin{aligned}&x<2\\&2<x<3\\&x>3\end{aligned}
x<2
2<x<3
x>3
4 Pick a test point for each interval.
For the interval x<2x<2:
Let's pick x=0x=0. Then, {0}^{2}-5\times 0+6<00
2
−5×0+6<0.
After simplifying, we get 6<06<0, which is false.
Drop this interval..
For the interval 2<x<32<x<3:
Let's pick x=\frac{5}{2}x=
25
. Then, {(\frac{5}{2})}^{2}-5\times \frac{5}{2}+6<0( 25) 2−5× 25+6<0.
After simplifying, we get -0.25<0−0.25<0, which is true.
Keep this interval..
For the interval x>3x>3:
Let's pick x=4x=4. Then, {4}^{2}-5\times 4+6<04 2 −5×4+6<0.
After simplifying, we get 2<02<0, which is false.
Drop this interval..
5 Therefore,
2<x<3
2<x<3
