1. Statement of the problem. The number line has four equally spaced points and the distance from the first to the last is 72 units. The point labeled x is at the midpoint between the second and third points from the left. We must find the distance from the first point to the point labeled x. 2. Formula and important rules. For equally spaced points, the number of equal segments equals the number of points minus 1. With 4 points there are 3 equal segments. The length of each segment is given by $$\frac{\text{total distance}}{\text{number of segments}}$$. 3. Compute the length of one segment. $$s = \frac{72}{3}$$ To simplify, factor 72 as $3\cdot 24$ and cancel the common factor 3. $$\frac{72}{3} = \frac{3\cdot 24}{3} = \frac{\cancel{3}\cdot 24}{\cancel{3}} = 24$$ Thus each segment has length 24 units. 4. Find positions and the midpoint. If the first point is at distance 0 from itself, then the second point is at 24 and the third at 48. The midpoint between the second and third points is $$\frac{24+48}{2}$$. Combine and simplify by factoring 72 as $2\cdot 36$ and canceling the common factor 2. $$\frac{24+48}{2} = \frac{72}{2} = \frac{2\cdot 36}{2} = \frac{\cancel{2}\cdot 36}{\cancel{2}} = 36$$ Therefore the point labeled x is 36 units from the first point. 5. Final answer. $$x = 36$$