The problem states that the mean of the numbers 2, 5, 2x, and 7 is less than or equal to 5. We need to find the range of values of x that satisfy this condition.

1. Problem Description

The problem states that the mean of the numbers 2, 5, 2x, and 7 is less than or equal to

5. We need to find the range of values of x that satisfy this condition.

2. Solution Steps

The mean of a set of numbers is the sum of the numbers divided by the number of elements in the set. In this case, the mean of 2, 5, 2x, and 7 is given by:

$\frac{2 + 5 + 2x + 7}{4}$

The problem states that this mean is less than or equal to

5. So we can write the inequality:

$\frac{2 + 5 + 2x + 7}{4} \le 5$

First, simplify the numerator:

$\frac{14 + 2x}{4} \le 5$

Multiply both sides of the inequality by 4:

$14 + 2x \le 20$

Subtract 14 from both sides:

$2x \le 20 - 14$

$2x \le 6$

Divide both sides by 2:

$x \le \frac{6}{2}$

$x \le 3$

3. Final Answer

The range of values for x is $x \le 3$.

The answer is A.