To solve the equation \( 5x - 5 = 10(2x - 7) \), follow these steps:

1. **Expand the right-hand side**:
   \[
   5x - 5 = 10 \times 2x - 10 \times 7
   \]
   \[
   5x - 5 = 20x - 70
   \]

2. **Move all terms involving \(x\) to one side**:
   Subtract \(5x\) from both sides:
   \[
   -5 = 20x - 70 - 5x
   \]
   Simplify:
   \[
   -5 = 15x - 70
   \]

3. **Isolate the \(x\) term**:
   Add 70 to both sides:
   \[
   -5 + 70 = 15x
   \]
   Simplify:
   \[
   65 = 15x
   \]

4. **Solve for \(x\)**:
   Divide both sides by 15:
   \[
   x = \frac{65}{15}
   \]
   Simplify the fraction:
   \[
   x = \frac{13}{3}
   \]

So, the solution is \( x = \frac{13}{3} \).

Would you like a detailed explanation on any specific part?

Here are 5 related questions you can explore:
1. How do you solve linear equations involving fractions?
2. What are the steps for solving equations with variables on both sides?
3. Can you solve the equation \( 7x - 3 = 5x + 9 \)?
4. How do you check if your solution to an equation is correct?
5. What is the best way to simplify algebraic expressions?

**Tip**: Always double-check your work by plugging your solution back into the original equation!

Learn how to solve the linear equation 5x - 5 = 10(2x - 7) with a detailed step-by-step solution. This problem focuses on key algebraic concepts like the distributive property and solving linear equations, ideal for students in Grades 7-9.

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