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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #36594)