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


Question

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

Options

A) x \(\leq\) 3

B) x \(\geq\) 3

C) x < 3

D) x > 3

The correct answer is B.

Explanation:

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


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Dicussion (1)

  • 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

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