To solve the equation \( 4x + 18 - 6x = 3x - 7 \), follow these steps:

### Step 1: Combine like terms
On the left-hand side, combine the terms involving \(x\):
\[
4x - 6x + 18 = 3x - 7
\]
This simplifies to:
\[
-2x + 18 = 3x - 7
\]

### Step 2: Move all terms involving \(x\) to one side
To isolate \(x\), move the \(3x\) from the right-hand side to the left-hand side by subtracting \(3x\) from both sides:
\[
-2x - 3x + 18 = -7
\]
This simplifies to:
\[
-5x + 18 = -7
\]

### Step 3: Move the constant term to the other side
Next, subtract 18 from both sides:
\[
-5x = -7 - 18
\]
Simplifying the right-hand side:
\[
-5x = -25
\]

### Step 4: Solve for \(x\)
Finally, divide both sides by \(-5\):
\[
x = \frac{-25}{-5}
\]
\[
x = 5
\]

Thus, the solution is \(x = 5\).

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. What happens if you move the constants first before combining like terms?
2. How would the equation change if the coefficients were fractions?
3. What are the possible scenarios when solving a linear equation with no solutions?
4. How can you verify the solution by substituting \(x = 5\) back into the original equation?
5. What is the difference between solving an equation with one variable versus multiple variables?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it's correct!

Learn how to solve the linear equation 4x + 18 - 6x = 3x - 7 through detailed steps, covering algebraic concepts like combining like terms and isolating variables. This guide is suitable for students in Grades 6-8 and provides an in-depth solution.

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