Find the value of x if the arithmetic means of 3 and 3×+5 is 8

To solve for \( x \), we are given that the arithmetic mean of 3 and \( 3x + 5 \) is 8. The formula for the arithmetic mean of two numbers \( a \) and \( b \) is:

\[
\text{Arithmetic Mean} = \frac{a + b}{2}
\]

Here, \( a = 3 \) and \( b = 3x + 5 \), and the arithmetic mean is given as 8. So, we set up the equation:

\[
\frac{3 + (3x + 5)}{2} = 8
\]

Now, simplify and solve for \( x \):

\[
\frac{3 + 3x + 5}{2} = 8
\]

\[
\frac{8 + 3x}{2} = 8
\]

Multiply both sides of the equation by 2 to eliminate the denominator:

\[
8 + 3x = 16
\]

Subtract 8 from both sides:

\[
3x = 8
\]

Now, divide by 3:

\[
x = \frac{8}{3}
\]

Thus, the value of \( x \) is \( \frac{8}{3} \).

Would you like more details, or do you have any questions?

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Here are 5 related questions to expand your understanding:
1. What is the arithmetic mean of two other variables, \( a \) and \( b \), if the sum of their arithmetic means equals 10?
2. How would the solution change if the arithmetic mean given were a different number?
3. Can you solve for \( x \) if the arithmetic mean of 4 and \( 2x + 7 \) is 6?
4. What is the formula for the arithmetic mean of three numbers?
5. How can arithmetic means be used to solve problems in statistics?

**Tip:** Always check your final answer by plugging it back into the original equation to ensure it satisfies the condition.

Find the value of x if the arithmetic mean of 3 and 3x + 5 is 8.

Learn how to find the value of x when the arithmetic mean of 3 and 3x + 5 equals 8. This problem covers important concepts in algebra and the arithmetic mean formula, suitable for students in Grades 6-8. Follow the step-by-step solution to understand how to solve linear equations.

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