Let's solve the equation step by step:

The given equation is:

\[
3(q-4) + 2q = q - 8 + 6(q + 2)
\]

### Step 1: Expand both sides
Expand the terms on both sides:

\[
3(q-4) = 3q - 12
\]
\[
6(q+2) = 6q + 12
\]

Substitute these into the equation:

\[
3q - 12 + 2q = q - 8 + 6q + 12
\]

### Step 2: Combine like terms
On the left side, combine \(3q\) and \(2q\):

\[
5q - 12
\]

On the right side, combine \(q\) and \(6q\), and combine \(-8\) and \(12\):

\[
7q + 4
\]

Now the equation becomes:

\[
5q - 12 = 7q + 4
\]

### Step 3: Move all terms with \(q\) to one side
Subtract \(5q\) from both sides:

\[
-12 = 2q + 4
\]

### Step 4: Solve for \(q\)
Subtract 4 from both sides:

\[
-12 - 4 = 2q
\]
\[
-16 = 2q
\]

Now divide both sides by 2:

\[
q = \frac{-16}{2} = -8
\]

### Final Answer:
\[
q = -8
\]

Would you like any further explanation or details on this? 

Here are five related questions to expand this topic:
1. How do you solve equations with variables on both sides?
2. What is the distributive property in algebra?
3. How do you simplify complex expressions?
4. How can you check your solution to an equation?
5. How do you solve multi-step linear equations?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies both sides!

Learn how to solve the linear equation 3(q-4) + 2q = q - 8 + 6(q + 2) with a detailed step-by-step approach. This problem covers algebraic concepts such as the distributive property and combining like terms, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation