To solve for \( x \) in the equation \( y = 3x + 7xz \), follow these steps:

1. **Factor out \( x \) from the terms on the right-hand side:**

   \[
   y = x(3 + 7z)
   \]

2. **Solve for \( x \) by dividing both sides by \( (3 + 7z) \):**

   \[
   x = \frac{y}{3 + 7z}
   \]

Thus, the solution is:

\[
x = \frac{y}{3 + 7z}
\]

Would you like more details on the steps? Here are some related questions to further explore:

1. How does factoring help in solving equations?
2. What happens if \( z = -\frac{3}{7} \) in this equation?
3. What are the limitations when solving for \( x \) if the denominator is zero?
4. Can this equation be expressed in terms of different variables?
5. How can this method apply to other similar equations?

**Tip:** Always check for values that make the denominator zero, as this would make the solution undefined.

Learn how to solve for x in the algebraic equation y = 3x + 7xz by factoring and simplifying. This step-by-step solution covers key concepts in algebra such as factoring common terms and solving linear equations. Suitable for students in Grades 9-10.

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