Let's solve the equation \(3(2x + 1) - 4x = 2x + 3\).

### Step 1: Distribute the \(3\) on the left-hand side.
\[
3 \cdot 2x + 3 \cdot 1 - 4x = 2x + 3
\]
\[
6x + 3 - 4x = 2x + 3
\]

### Step 2: Combine like terms on the left-hand side.
\[
(6x - 4x) + 3 = 2x + 3
\]
\[
2x + 3 = 2x + 3
\]

### Step 3: Subtract \(2x\) from both sides to simplify.
\[
3 = 3
\]

### Conclusion:
The equation simplifies to \(3 = 3\), which is a true statement. This means that the equation is an identity and holds true for all values of \(x\). Therefore, the equation has **infinitely many solutions**.

Would you like more details or have any questions?

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Here are five related questions:
1. What does it mean when an equation simplifies to a true statement like \(3 = 3\)?
2. How can you recognize an identity equation before solving it completely?
3. What are the different types of solutions an equation can have?
4. How would you graphically represent an equation with infinitely many solutions?
5. What is the difference between a conditional equation and an identity?

**Tip:** When solving an equation, if you eliminate the variable and end up with a true statement, it means the equation has infinitely many solutions.

Learn how to solve the linear equation 3(2x + 1) - 4x = 2x + 3 with a step-by-step solution. This problem involves applying the distributive property and combining like terms. Suitable for students in Grades 6-8.

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