Let's solve the equation step by step:

\[
4(3x + 6) + 8 = 16 - (10x - 5) + 24
\]

### Step 1: Distribute the constants on both sides.
On the left-hand side:
\[
4(3x + 6) = 12x + 24
\]
So the equation becomes:
\[
12x + 24 + 8 = 16 - 10x + 5 + 24
\]

### Step 2: Simplify both sides.
On the left-hand side:
\[
12x + 24 + 8 = 12x + 32
\]
On the right-hand side:
\[
16 - 10x + 5 + 24 = 45 - 10x
\]
The equation is now:
\[
12x + 32 = 45 - 10x
\]

### Step 3: Move all terms involving \(x\) to one side and constants to the other.
Add \(10x\) to both sides:
\[
12x + 10x + 32 = 45
\]
This simplifies to:
\[
22x + 32 = 45
\]

### Step 4: Isolate the term with \(x\).
Subtract 32 from both sides:
\[
22x = 45 - 32
\]
\[
22x = 13
\]

### Step 5: Solve for \(x\).
Divide both sides by 22:
\[
x = \frac{13}{22}
\]

So, the solution is:
\[
x = \frac{13}{22}
\]

Would you like more details or have any questions?

Here are some related questions to explore:
1. How do you simplify equations with distribution?
2. Can you explain how to isolate variables in different types of equations?
3. What happens if both sides of the equation contain fractions?
4. How would the solution change if the coefficients were different?
5. Can you graph the equation to visualize the solution?

**Tip:** Always combine like terms first to simplify the equation before solving!

Learn how to solve the linear equation 4(3x + 6) + 8 = 16 - (10x - 5) + 24 with step-by-step guidance. This solution covers key algebraic concepts such as the distributive property and combining like terms. Ideal for students in Grades 8-10.

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