Let's solve the equation:

\[
4x - 3 = -2x + 9
\]

### Step 1: Move all the terms involving \(x\) to one side.
Add \(2x\) to both sides:

\[
4x + 2x - 3 = 9
\]

\[
6x - 3 = 9
\]

### Step 2: Move the constant term to the other side.
Add 3 to both sides:

\[
6x = 12
\]

### Step 3: Solve for \(x\).
Divide both sides by 6:

\[
x = \frac{12}{6} = 2
\]

So, the solution is \(x = 2\).

Would you like further details or explanations?

Here are 5 related questions:
1. How do you solve equations with variables on both sides?
2. What happens if there are fractions in the equation?
3. Can we use different methods to solve this equation, like substitution?
4. How do you check if a solution is correct?
5. How do you solve equations with more than one variable?

**Tip:** Always check your solution by substituting it back into the original equation!

Discover how to solve the linear equation 4x - 3 = -2x + 9 using basic algebraic steps. This detailed solution demonstrates key concepts such as moving terms across the equation and solving for x. Ideal for students in Grades 7-8.

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