Question 1206365
abs(x-697) <= 5 is the equation you want.


this equation can be split into two parts.


when (x-697) is positive, it becomes (x-697) <= 5.


when (x-697) is negative, it becomes -(x-697) <= 5


that's because, by definition, abs(x) = x when x is positive and equals -x when x is negative.


x represents the expression within the absolute value sign.


x by itself is an expression within the absolute value sign.
x - 697 is an expression within the absolute value sign.


absolute value of an expression can be written as abs(x) or it can be written as |x|, where the vertical lines indicated that the absolute value expression is between them.


you start with abs(x-697) <= 5


when (x-697) is positive, the equation becomes (x-697) <= 5


when (x-697) is negative, the equation becomes -(x-697) <= 5
if you multiply both sides of this inequality by -1, the inequality reverses and you are left with (x-697) >= -5.


to solve, start with (x-697) <= 5
add 697 to both sides of that inequality to get x <= 697 + 5 which simplifies to x <= 702.


next start with -(x-697) <= 5.
multiply both sides of that inequality by -2 to get (x-697) >= -5.
add 697 to both sides of that inequality to get x >= 697 - 5 which simplifies to x >= 692.


abs(x - 697) <= 5 means 692 <= x <= 702.


the highest guess would be 702 and the lowest guess would be 692.
those guesses and any guess in between provides a chance to win the truck.