What is the solution to the inequality |X-4<37
-7 O 1 OX<-7 or x <-1
O x> 1 or x = 7

x<7 or x>1

Step-by-step explanation:

The given inequality is

|x-4|<37

By the definition of the absolute value function, we get

x-4<3 or -(x-4)<3

We divide both sides of the inequality on the right by -1 and reverse the sign.

x-4<3 or x-4>-3

We add 4 to both sides of the equation to get:

x-4+4<3+4 or x-4+4>-3+4

x<7 or x>1