Question

If the distance from 0 to x on a number line is greater than 2, then -2+x is positive. True or false

Answer 1

The absolute value of x, written as |x|, is the distance from x to 0 on the number line.

If the distance is larger than 2, then we know
|x| > 2

If |x| > 2, then either x > 2 or x < -2

If x > 2, then we can subtract 2 from both sides to get...
x > 2
x-2 > 2-2
x-2 > 0
x + (-2) > 0
-2 + x > 0

So -2+x is positive. The original statement is true.

Answer 2

The above answer is not correct. You must also consider the possibility of x<-2 and if x is less than -2, then -2+x<0 so we cannot say for certain that -2+x>0 so the answer is FALSE