To solve this problem, let's break down the statement step-by-step and translate it into an algebraic equation.

Problem Analysis

The question states:

"Six fewer than 30 times a number is five more than eight times the number."

Let’s represent the unknown number as $x$.

1. "30 times a number" can be written as $30x$.
2. "Six fewer than 30 times a number" means we subtract 6 from $30x$, which gives us $30x - 6$.
3. "Eight times the number" is $8x$.
4. "Five more than eight times the number" means we add 5 to $8x$, resulting in $8x + 5$.

According to the problem, these two expressions are equal: $30x - 6 = 8x + 5$

Solving the Equation

Now, let's solve for $x$.

1. Move all terms involving $x$ to one side of the equation: $30x - 8x = 5 + 6$

2. Simplify both sides: $22x = 11$

3. Divide by 22 to isolate $x$: $x = \frac{11}{22} = \frac{1}{2}$

Answer

The value of $x$ is $\frac{1}{2}$.

Conclusion

The correct answer is: $\boxed{\frac{1}{2}}$

Would you like a detailed explanation of any step or have any questions?

Here are some related questions to deepen understanding:

1. What would the solution be if the problem stated "ten fewer than 40 times a number is equal to twelve times the number plus four"?
2. How do you interpret phrases like "more than" or "fewer than" when forming algebraic expressions?
3. How would the equation change if we doubled the number in all terms of the problem?
4. What is the process for checking if your solution is correct in such word problems?
5. How would we solve if "six fewer than 30 times a number" was instead "30 times a number minus 6 times another number"?

Tip: When solving word problems, translate each phrase step-by-step into an equation. This makes it easier to avoid mistakes.