Write the statement using absolute value notation:
the distance between x and 4 is 3

Ix-4I=3 
The supreme esteem condition above implies that x-4 is equivalent to 3, OR, that x-4 is equivalent to - 3. 
On the off chance that x-4=3, then x=7. On the off chance that x-4=-3, then x=1. 
Presently envision the number line with the numbers 1 and 7 set apart with a dab. 
The number 4 is in the focal point of that fragment. What's more, the numbers 1 and 7 are at a separation of precisely 3 units of the number 4 which is at the middle. 
That is precisely what the outright esteem condition is requesting that you discover. Which numbers are inside a separation of 3 units of 4. Also, your answer is x=1 and x=7.