To solve the equation \(-7x = 15 - 2x\), we need to isolate \(x\). Here’s the step-by-step process:

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

\[
-7x + 2x = 15
\]

\[
-5x = 15
\]

### Step 2: Solve for \(x\).
Now, divide both sides of the equation by \(-5\):

\[
x = \frac{15}{-5}
\]

\[
x = -3
\]

### Solution:
The solution is \(x = -3\).

Would you like further clarification on any of the steps? Here are five related questions to deepen your understanding:

1. How would the solution change if the constant term was different?
2. What if the equation was \(-7x = 15 + 2x\)?
3. How can you verify the solution by substituting back into the original equation?
4. What if there were fractions involved instead of integers?
5. How does the process change if the equation was quadratic?

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

Learn how to solve the linear equation -7x = 15 - 2x with a clear, step-by-step explanation. This problem involves fundamental algebraic concepts such as combining like terms and isolating variables. Ideal for students in Grades 7-9.

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