Question

Express the given geometric statement about numbers on the number line algebraically, using absolute values.
x is within 2 units of -1

Answer 1

|x-(-1)|<2
or
|x+1|<2

the abslute value of a difference is a distance; the <2 is the interpretation of "within 2 units" (this idea is easier to explain with absolute value equations)

Answer 2

here is the equation version of "x is exactly 2 units from -1" we can figure this number out by simply adding and subtracting: 2 units to the left of -1 is -3; 2 units to the right of -1 is 1... now see that -3 and 1 satisfy the following:

|x+1|=2

here it is on the number line