If the distance between the points (x, –1) and (3, 2) is 5, then the value of x is

The distance between two points (x1, y1) and (x2, y2) in a plane is given by the formula:

d = sqrt[(x2 - x1)² + (y2 - y1)²]

Here, we are given that the distance d between the points (x, -1) and (3, 2) is 5. Substituting these values into the formula, we get:

5 = sqrt[(3 - x)² + (2 - (-1))²]

Squaring both sides to get rid of the square root, we get:

25 = (3 - x)² + 9

Rearranging the equation, we get:

(3 - x)² = 25 - 9

(3 - x)² = 16

Taking the square root of both sides, we get two possible solutions:

3 - x = 4 or 3 - x = -4

Solving these equations for x, we get:

x = 3 - 4 = -1 or x = 3 - (-4) = 7

So, the possible values of x are -1 and 7.