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Let's solve the given equation step-by-step.

The equation is:
\[ 3 + 4x - (x - 2) = 3x + 4 \]

First, simplify the left-hand side by distributing the negative sign through the parentheses:
\[ 3 + 4x - x + 2 = 3x + 4 \]

Combine like terms on the left-hand side:
\[ 3 + 2 + 4x - x = 3x + 4 \]
\[ 5 + 3x = 3x + 4 \]

Next, subtract \( 3x \) from both sides to isolate the constant terms:
\[ 5 = 4 \]

This results in a contradiction, indicating that there is no value of \( x \) that satisfies the equation. Thus, the equation has no solution.

Would you like more details or have any questions?

Here are some related questions to expand your understanding:
1. What does it mean when an equation has no solution?
2. How can we verify if a solution exists for a given equation?
3. What are the steps to solve a linear equation?
4. Can you provide another example of an equation with no solution?
5. How does the distributive property work in simplifying equations?

**Tip:** Always check your work by substituting the solution back into the original equation to ensure it satisfies all parts of the equation.

Learn how to solve the equation 3 + 4x - (x - 2) = 3x + 4 with a step-by-step explanation. This algebraic problem demonstrates the use of the distributive property and solving linear equations with no solution. Suitable for Grades 8-10.

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