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The solution to the equation \( 7\left(7x + \frac{1}{2}\right) - 5\left(5x - \frac{1}{2}\right) = 0 \) is:

\[
x = -0.25
\]

Would you like more details or have any further questions?

Here are 5 related questions to expand your understanding:

1. How would the solution change if the equation had different coefficients inside the parentheses?
2. What is the significance of distributing constants in solving linear equations?
3. How would this equation look in a different form, like standard form \(Ax + B = 0\)?
4. What happens if we introduce another variable into this type of equation?
5. How can we verify the solution graphically?

**Tip:** Always simplify and check your equation step by step to avoid errors while distributing and combining terms!

Solve the equation: 7(7x + 1/2) - 5(5x - 1/2) = 0

Learn how to solve the linear equation 7(7x + 1/2) - 5(5x - 1/2) = 0 with step-by-step guidance. This problem demonstrates the use of the distributive property and basic algebraic principles, making it ideal for students in Grades 8-10.

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