https://file.aiquickdraw.com/mathbot/file/1725465823757erd7mj6z.jpg

The problem in the image asks to solve the equation:

\[
2x + 3 = 6 + 4x
\]

Let's solve this step by step.

### Step 1: Simplify the equation
Subtract \(2x\) from both sides to start isolating \(x\):

\[
2x + 3 - 2x = 6 + 4x - 2x
\]

This simplifies to:

\[
3 = 6 + 2x
\]

### Step 2: Isolate the variable term
Next, subtract 6 from both sides to isolate the term with \(x\):

\[
3 - 6 = 2x
\]

This simplifies to:

\[
-3 = 2x
\]

### Step 3: Solve for \(x\)
Divide both sides by 2 to solve for \(x\):

\[
x = \frac{-3}{2}
\]

Thus, the solution is:

\[
x = -\frac{3}{2}
\]

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

### Related Questions:
1. How would the solution change if the equation was \(2x + 3 = 6 - 4x\)?
2. What is the significance of isolating the variable when solving an equation?
3. How would you check if your solution for \(x\) is correct?
4. What if the equation was \(2x + 3 = 6 + 4x + 2\), how would the steps change?
5. Can you explain what happens if both sides of the equation are multiplied by a number before solving?

### Tip:
Always double-check your solution by substituting the value of \(x\) back into the original equation to ensure both sides are equal.

Explore how to solve the linear equation 2x + 3 = 6 + 4x with a clear step-by-step approach. This problem involves key algebraic concepts like isolating the variable and balancing equations. Ideal for students in Grades 6-8.

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