Question

1. the average of 8, 14, and x is 11. what is the value of x? 11 8 12 10

Explanation:

Step1: Use the average formula

The formula for the average of a set of numbers \(a,b,c\) is \(\frac{a + b+ c}{3}\). Here, \(a = 8\), \(b = 14\), \(c=x\), and the average is \(11\). So, \(\frac{8 + 14+x}{3}=11\).

Step2: Solve the equation for \(x\)

Multiply both sides of the equation \(\frac{8 + 14+x}{3}=11\) by \(3\) to get \(8 + 14+x=11\times3\). Then, \(8 + 14+x = 33\). Combine like - terms: \(22+x=33\). Subtract \(22\) from both sides: \(x=33 - 22\).

Answer:

\(x = 9\) (Since there is no option with \(9\) in the provided choices, there might be an error in the problem setup or options. But following the calculation \(\frac{8+14 + x}{3}=11\Rightarrow22 + x=33\Rightarrow x = 11\) if we assume a miscalculation in step - by - step. Re - checking: \(\frac{8+14 + 11}{3}=\frac{33}{3}=11\))
So the answer is \(11\) (assuming a miscalculation in the initial step - by - step where \(8+14 + 11=33\) and \(\frac{33}{3}=11\))