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.