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To determine how many solutions the equation \( 2x + 3 = 4x + 2 \) has, let's solve it step-by-step.

Starting with the given equation:
\[ 2x + 3 = 4x + 2 \]

1. Subtract \( 2x \) from both sides:
\[ 3 = 2x + 2 \]

2. Subtract 2 from both sides:
\[ 1 = 2x \]

3. Divide both sides by 2:
\[ x = \frac{1}{2} \]

Since we have found a single value for \( x \) that satisfies the equation, the equation has exactly **1 solution**.

The correct answer is:
- 1 solution

Would you like more details or have any questions about this solution?

Here are 5 related questions to expand your understanding:
1. How do you determine if a linear equation has no solutions?
2. What does it mean for an equation to have many solutions?
3. Can you provide an example of a linear equation with no solutions?
4. Can you provide an example of a linear equation with infinitely many solutions?
5. How does the graph of a linear equation with one solution differ from that of an equation with no solutions or infinitely many solutions?

**Tip:** When solving linear equations, isolating the variable on one side of the equation is a key step to finding the solution.

How many solutions does the equation 2x + 3 = 4x + 2 have?

Learn how to solve the linear equation 2x + 3 = 4x + 2 with a step-by-step solution. This problem covers key algebraic concepts such as isolating variables and using the properties of equality. Ideal for students in Grades 7-9.

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