Explanation

Since the point is on the x-axis, its coordinates are (x, 0).

To find the point equidistant from (0, 1) and (3, 1), set up the equation:

√((x - 0)² + (0 - 1)²) = √((x - 3)² + (0 - 1)²)

Simplify the equation:

√(x² + 1) = √((x - 3)² + 1)

Square both sides:

x² + 1 = (x - 3)² + 1

Expand and simplify:

x² = x² - 6x + 9

Subtract x² from both sides:

0 = -6x + 9

Add 6x to both sides:

6x = 9

Divide by 6:

x = 9/6

x = 1.5

So, the point on the x-axis is:

(1.5, 0)