Question

If the distance between (b, 3) and (7, 3) is 3.5 units, find all possible values of b.

Answer 1

Use the distance formula:
d^2 = (y2 - y1)^2 + (x2 - x1)^2
where
d = distance
(x1, y1) and (x2, y2) = points

Thus,
3.5^2 = (3 - 3)^2 + (7 - b)^2
12.25 = 0 + 49 - 14b + b^2

Now solve for b.

Answer 2

Or, you can stop at:

3.5^2 = (3 - 3)^2 + (7 - b)^2

and you have

(b-7)^2 = 3.5^2
b-7 = ±3.5
b = 7±3.5

Answer 3

or, you can notice that they lie on the same horizontal line, so (b,3) is either 3.5 units to the right or to the left of (7,3)
so b = 7 ± 3.5

which is what Steve shows in his last line as well.