Let's solve the equation:

\[
3(2x + 9) + 12(4x - 8) = 55
\]

### Step 1: Distribute the constants.

First, distribute the \( 3 \) and \( 12 \) to terms inside the parentheses:

\[
3(2x + 9) = 6x + 27
\]
\[
12(4x - 8) = 48x - 96
\]

So the equation becomes:

\[
6x + 27 + 48x - 96 = 55
\]

### Step 2: Combine like terms.

Combine the \( x \)-terms and the constant terms:

\[
6x + 48x = 54x
\]
\[
27 - 96 = -69
\]

Now the equation is:

\[
54x - 69 = 55
\]

### Step 3: Isolate the \( x \)-term.

Add 69 to both sides of the equation to move the constant to the right side:

\[
54x = 55 + 69
\]
\[
54x = 124
\]

### Step 4: Solve for \( x \).

Divide both sides by 54:

\[
x = \frac{124}{54}
\]

Simplify the fraction:

\[
x = \frac{62}{27}
\]

So, the solution is:

\[
x = \frac{62}{27}
\]

Would you like further details on any steps? Here are some related questions:

1. How can you verify the solution by substituting \( x \) back into the original equation?
2. What is the importance of distributing constants in equations?
3. How do you simplify complex fractions like \( \frac{62}{27} \)?
4. What is the difference between combining like terms and isolating variables?
5. Can you express the solution \( x = \frac{62}{27} \) as a decimal?

**Tip:** When solving equations, always distribute and combine like terms first for simplification.

Learn how to solve the linear equation 3(2x + 9) + 12(4x − 8) = 55 with a step-by-step guide. This problem covers algebraic concepts such as the distributive property, combining like terms, and isolating variables. Suitable for students in Grades 8-10.

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