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To solve the equation \( 8(x + 1) = 5 - 2(8x + 6) \), follow these steps:

1. **Distribute** both sides of the equation:
   \[
   8x + 8 = 5 - 2(8x + 6)
   \]
   \[
   8x + 8 = 5 - 16x - 12
   \]

2. **Simplify** the right side of the equation by combining like terms:
   \[
   8x + 8 = -16x - 7
   \]

3. **Add** \(16x\) to both sides to move the \(x\) terms to one side:
   \[
   8x + 16x + 8 = -7
   \]
   \[
   24x + 8 = -7
   \]

4. **Subtract** 8 from both sides to isolate the term with \(x\):
   \[
   24x = -7 - 8
   \]
   \[
   24x = -15
   \]

5. **Divide** both sides by 24 to solve for \(x\):
   \[
   x = \frac{-15}{24}
   \]
   Simplify the fraction:
   \[
   x = \frac{-5}{8}
   \]

So, the solution is \( x = \frac{-5}{8} \).

Would you like any further details or have any questions?

Here are 5 related questions:
1. What happens if you add or subtract terms incorrectly during the solving process?
2. How would you solve a similar equation if it included a quadratic term (e.g., \(x^2\))?
3. How can you check if your solution to the equation is correct?
4. What is the process for solving an equation with fractions from the start?
5. How does the distributive property work when solving equations like this?

**Tip:** Always remember to combine like terms and simplify each side of the equation before moving terms across the equals sign. This helps avoid errors and makes the equation easier to solve.

Solve the following equation: 8(x + 1) = 5 - 2(8x + 6)

Learn how to solve the linear equation 8(x + 1) = 5 - 2(8x + 6) with a step-by-step solution. This problem demonstrates the use of the distributive property and properties of equality, making it suitable for students in Grades 7-10.

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