What is the average (arithmetic meani) of
, and ?

Ask by Powers Reid. in the United States

Mar 25,2025

Question

What is the average (arithmetic meani) of $$ 4 x+ $$ $$ 5,7 x-6 $$, and $$ -8 x+2 $$ ? $$ x+1 $$

UpStudy AI · Accepted Answer

We want to find the arithmetic mean of the three expressions
$$
4x+5,\quad 7x-6,\quad -8x+2.
$$

Step 1. Write the formula for the arithmetic mean:
$$
\text{Average} = \frac{(4x+5)+(7x-6)+(-8x+2)}{3}.
$$

Step 2. Combine like terms in the numerator:

Combine the $$x$$-terms:
$$
4x+7x-8x = 3x,
$$
and the constants:
$$
5-6+2=1.
$$
Thus, the numerator simplifies to:
$$
3x+1.
$$

Step 3. Write the simplified expression for the arithmetic mean:
$$
\text{Average} = \frac{3x+1}{3}.
$$

Step 4. The problem asks if the average is $$x+1$$. We set the arithmetic mean equal to $$x+1$$:
$$
\frac{3x+1}{3} = x+1.
$$

Step 5. Solve the equation:
Multiply both sides by 3:
$$
3x+1 = 3(x+1).
$$
Simplify the right-hand side:
$$
3x+1 = 3x+3.
$$
Subtract $$3x$$ from both sides:
$$
1 = 3.
$$

Since $$1=3$$ is a contradiction, there is no value of $$x$$ for which
$$
\frac{3x+1}{3} = x+1.
$$

Thus, the arithmetic mean of the three expressions is 
$$
\frac{3x+1}{3},
$$
which is not equal to $$x+1$$ for any value of $$x$$.
The arithmetic mean of the expressions $$4x+5$$, $$7x-6$$, and $$-8x+2$$ is $$\frac{3x+1}{3}$$, which is not equal to $$x+1$$.

What is the average (arithmetic meani) of
, and ?

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What is the average (arithmetic meani) of , and ?