The mean of the numbers 2, 5, 2x and 7 is less than or equal to 5. Find the range of the values of x

A.

x \(\leq\) 3

B.

x \(\geq\) 3

C.

x < 3

D.

x > 3

Correct answer is A

mean \(\leq\) 5; \(\frac{2 + 5 + 2x + 7}{4}\) \(\leq\) 5

= \(\frac{14 + 2x}{4} \leq 5\)

= 14 + 2x \(\leq\) 5 x 4

14 + 2x \(\leq\) 20 ; 2x \(\leq\) 20 - 14

2x \(\leq\) 20 - 14

2x \(\leq\) 6

x \(\leq\) \(\frac{6}{2}\)

x \(\leq\) 3