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The equation provided is:

\[
2x + 3(5x - 7) = 47
\]

Let’s solve it step-by-step.

### Step 1: Expand the equation
\[
2x + 3(5x - 7) = 47
\]
Distribute the \(3\) across the parentheses:
\[
2x + 15x - 21 = 47
\]

### Step 2: Combine like terms
\[
(2x + 15x) - 21 = 47
\]
\[
17x - 21 = 47
\]

### Step 3: Isolate the variable
Add 21 to both sides:
\[
17x = 47 + 21
\]
\[
17x = 68
\]

### Step 4: Solve for \(x\)
Divide both sides by 17:
\[
x = \frac{68}{17}
\]
\[
x = 4
\]

So, the correct solution is \(x = 4\).

Would you like further details or have any additional questions?

Here are 5 follow-up questions:
1. What would happen if the constant term on the right side of the equation changed?
2. How would the process differ if there were fractions instead of integers?
3. Can you solve an equation if it has terms involving \(x^2\) (quadratic terms)?
4. How would you graph the equation \(2x + 3(5x - 7) = 47\)?
5. How can we verify the solution by substituting back into the original equation?

**Tip:** Always simplify each step of an equation before solving for the unknown variable.

Learn how to solve the linear equation 2x + 3(5x - 7) = 47 with a detailed step-by-step solution. This problem focuses on basic algebra, including the distributive property and combining like terms. Suitable for students in Grades 7-9.

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