https://file.aiquickdraw.com/mathbot/file/1726103063823nfqfa1ph.jpg

The equation provided in the image is:

\[
6x + 2x - 9 = 47
\]

Let's solve it step by step:

### Step 1: Combine like terms
On the left-hand side, combine the terms involving \(x\):

\[
6x + 2x = 8x
\]

Now the equation becomes:

\[
8x - 9 = 47
\]

### Step 2: Isolate the variable term
Add 9 to both sides to move the constant to the right-hand side:

\[
8x = 47 + 9
\]
\[
8x = 56
\]

### Step 3: Solve for \(x\)
Divide both sides by 8 to isolate \(x\):

\[
x = \frac{56}{8}
\]
\[
x = 7
\]

### Step 4: Check the solution
Substitute \(x = 7\) back into the original equation to verify:

\[
6(7) + 2(7) - 9 = 47
\]
\[
42 + 14 - 9 = 47
\]
\[
56 - 9 = 47
\]
\[
47 = 47
\]

The solution is correct: \(x = 7\).

Do you need further details or explanations on this solution?

Here are five related questions:
1. How do you solve multi-step equations with fractions?
2. What is the process of isolating a variable in an equation?
3. How do you solve equations that contain parentheses?
4. What does it mean to check a solution, and why is it important?
5. How do you solve equations with variables on both sides?

**Tip:** Always remember to combine like terms before starting to isolate the variable!

Learn how to solve the linear equation 6x + 2x - 9 = 47 step by step. This problem involves key algebra concepts like combining like terms and isolating the variable. Ideal for students in Grades 6-8.

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