We can solve the equation \( 8(x + 1) = 5 - 2(8x + 6) \) step by step.

### Step 1: Expand both sides of the equation
On the left-hand side, distribute the \( 8 \):
\[
8(x + 1) = 8x + 8
\]

On the right-hand side, distribute the \( -2 \) across \( (8x + 6) \):
\[
-2(8x + 6) = -16x - 12
\]

Now the equation becomes:
\[
8x + 8 = 5 - 16x - 12
\]

### Step 2: Simplify the right-hand side
Combine like terms on the right-hand side:
\[
5 - 12 = -7
\]
So, the equation is now:
\[
8x + 8 = -7 - 16x
\]

### Step 3: Move all \( x \)-terms to one side
Add \( 16x \) to both sides to move the \( x \)-terms together:
\[
8x + 16x + 8 = -7
\]
\[
24x + 8 = -7
\]

### Step 4: Move constants to the other side
Subtract 8 from both sides:
\[
24x = -7 - 8
\]
\[
24x = -15
\]

### Step 5: Solve for \( x \)
Divide both sides by 24:
\[
x = \frac{-15}{24} = \frac{-5}{8}
\]

Thus, the solution is:
\[
x = \frac{-5}{8}
\]

Would you like further clarification on any of the steps?

### Related questions:
1. How do you solve equations involving fractions?
2. What is the method to solve systems of linear equations?
3. Can you explain how to solve equations with multiple variables?
4. How do you solve quadratic equations?
5. What are the steps to solve equations with exponents?

### Tip: Always simplify both sides of an equation as much as possible before solving.

Learn how to solve the linear equation 8(x + 1) = 5 − 2(8x + 6) with step-by-step instructions. This problem covers key algebraic concepts such as distribution and solving for x. Suitable for students in Grades 7-9.

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