If x is an integer, what is the value of x? (1) x^2 - 4x + 3

There is one more simple method to solve inequalities:
x2−4x+3>0
Sol:
Step 1: Equate the quadratic equation to 0 : x2−4x+3 = 0 which gives us two values for x , x= 3 , x=1

Step 2 : Now draw number line with the roots there and mark + ,- alternately like below:

_______+_______ 1 ________-_________3 __________+_________
Step 3: If the inequality is > then we will select + range . If the inequality is < then we will select - range above.

Step 4: Here as the inequality is > we will chose + ranges from the number line.
x<1 and x>3
Step 5: If the inequality above was < we will simply choose the range where - is present:
1<x<3
Note: Always start marking + ,- with + only from the left of the 1st root you have found.
If inequality is > choose + range
If inequality is < choose -ve range