To find the average of the expressions [tex]\(2x + 5\)[/tex], [tex]\(5x - 6\)[/tex], and [tex]\(-4x + 2\)[/tex], we need to follow these steps:
1. Sum the expressions:
- First expression: [tex]\(2x + 5\)[/tex]
- Second expression: [tex]\(5x - 6\)[/tex]
- Third expression: [tex]\(-4x + 2\)[/tex]
Sum of these expressions is:
[tex]\[
(2x + 5) + (5x - 6) + (-4x + 2)
\][/tex]
2. Combine like terms:
Combine the [tex]\(x\)[/tex]-terms and the constant terms separately:
[tex]\[
(2x + 5x - 4x) + (5 - 6 + 2)
\][/tex]
Simplifying these,
[tex]\[
(2x + 5x - 4x) = (3x)
\][/tex]
[tex]\[
(5 - 6 + 2) = (1)
\][/tex]
Therefore, the sum of the expressions is:
[tex]\[
3x + 1
\][/tex]
3. Calculate the average:
To find the average, we divide the sum by the number of expressions, which is 3:
[tex]\[
\text{Average} = \frac{3x + 1}{3}
\][/tex]
4. Simplify the average:
Divide both terms in the numerator by 3:
[tex]\[
\frac{3x}{3} + \frac{1}{3} = x + \frac{1}{3}
\][/tex]
Thus, the average of the expressions [tex]\(2x + 5\)[/tex], [tex]\(5x - 6\)[/tex], and [tex]\(-4x + 2\)[/tex] is:
[tex]\[
x + \frac{1}{3}
\][/tex]
The correct answer is [tex]\(\boxed{x + \frac{1}{3}}\)[/tex]. So the correct choice is:
C. [tex]\(x + \frac{1}{3}\)[/tex]
