The equation given is:

$4x + 5 - 2x + 6 = 3x - 4$

Let's simplify it step-by-step:

1. Combine like terms on the left side: $(4x - 2x) + (5 + 6) = 3x - 4$ $2x + 11 = 3x - 4$

2. Move all terms involving $x$ to one side and constant terms to the other: $2x - 3x = -4 - 11$ $-x = -15$

3. Divide by $-1$ to solve for $x$: $x = 15$

So, the solution is: $x = 15$

Would you like further details or have any questions?

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Here are some related questions you might explore:

1. How do you solve similar linear equations with variables on both sides?
2. What are the steps for isolating the variable in an equation?
3. How do you check if your solution is correct by substituting back into the original equation?
4. What happens if there are fractions in the equation?
5. How can you solve equations with multiple variables?

Tip: Always simplify each side of an equation as much as possible before moving terms around.