To solve the equation \(4x - 3 = -5x + 6\), we need to isolate the variable \(x\). Here are the steps:

1. **Combine like terms involving \(x\)** on one side of the equation by adding \(5x\) to both sides:

\[
4x + 5x - 3 = -5x + 5x + 6
\]

This simplifies to:

\[
9x - 3 = 6
\]

2. **Isolate the term involving \(x\)** by adding \(3\) to both sides:

\[
9x - 3 + 3 = 6 + 3
\]

Simplifying this, we get:

\[
9x = 9
\]

3. **Solve for \(x\)** by dividing both sides by 9:

\[
x = \frac{9}{9}
\]

\[
x = 1
\]

So, the solution to the equation \(4x - 3 = -5x + 6\) is \(x = 1\).

### Would you like more details, or do you have any questions?

Here are some related questions that you might find interesting:

1. How would the solution change if the equation was \(4x - 3 = -5x + 16\)?
2. What are the steps to solve an equation involving fractions, such as \(\frac{3x}{2} - 4 = \frac{x}{3} + 5\)?
3. Can you demonstrate solving a quadratic equation, like \(x^2 - 4x - 5 = 0\)?
4. How do we solve equations involving absolute values, such as \(|2x - 3| = 5\)?
5. What is the process for solving a system of linear equations with two variables, like \(2x + y = 10\) and \(x - 3y = -2\)?

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

Learn how to solve the equation 4x - 3 = -5x + 6 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving linear equations and combining like terms. Suitable for students in Grades 7-9.

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