Solve the equation  8(82x)+39(8x)−5=0
for  x
.

To solve the equation \( 8(82x) + 39(8x) - 5 = 0 \) for \( x \), let's break it down step by step.

1. **Distribute the constants:**
   \[
   8 \cdot 82x + 39 \cdot 8x - 5 = 0
   \]
   This simplifies to:
   \[
   656x + 312x - 5 = 0
   \]

2. **Combine like terms:**
   \[
   (656x + 312x) - 5 = 0
   \]
   \[
   968x - 5 = 0
   \]

3. **Isolate the variable \( x \):**
   Add 5 to both sides:
   \[
   968x = 5
   \]
   Now, divide both sides by 968:
   \[
   x = \frac{5}{968}
   \]

4. **Simplify the fraction** (if possible):
   The fraction \( \frac{5}{968} \) is already in its simplest form since 5 and 968 have no common factors other than 1.

So, the solution is:
\[
x = \frac{5}{968}
\]

Would you like more details or have any questions?

### Related Questions
1. How would the solution change if the equation was \(8(82x) + 39(8x) + 5 = 0\)?
2. What is the decimal approximation of \( \frac{5}{968} \)?
3. How can you verify that \( x = \frac{5}{968} \) is a solution to the equation?
4. What would happen if one of the coefficients in the original equation were negative?
5. How do you factor out common terms in a more complex equation?

### Tip
Always double-check the distribution step in equations, as it's easy to make errors that affect the final result.

Learn how to solve the equation 8(82x) + 39(8x) - 5 = 0 for x with detailed steps and a clear explanation. This problem involves algebraic concepts such as distributive property, combining like terms, and solving linear equations. Suitable for Grades 7-9 students.

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