To solve the equation \( 4(2x - 5) = 8x - 5 \), let's go step by step:

### Step 1: Expand the left-hand side
Distribute the \( 4 \) across \( (2x - 5) \):
\[
4(2x - 5) = 4 \cdot 2x - 4 \cdot 5 = 8x - 20
\]
So the equation becomes:
\[
8x - 20 = 8x - 5
\]

### Step 2: Simplify the equation
Now, subtract \( 8x \) from both sides:
\[
8x - 20 - 8x = 8x - 5 - 8x
\]
This simplifies to:
\[
-20 = -5
\]

### Step 3: Interpret the result
Since \( -20 \neq -5 \), this is a contradiction. Therefore, the original equation has **no solution**.

### Final Conclusion:
The equation is inconsistent, meaning there is no value of \( x \) that satisfies the equation.

Do you want more details, or do you have any questions?

Here are some related questions:
1. What does it mean when an equation has no solution?
2. Can you give an example of a similar equation that does have a solution?
3. How do you recognize an equation with infinite solutions?
4. What are some strategies for solving more complex linear equations?
5. How do contradictions in equations arise?

**Tip:** Always simplify both sides of an equation first to avoid unnecessary complications later.

Learn how to solve the linear equation 4(2x - 5) = 8x - 5 with a step-by-step explanation. This problem illustrates key algebraic concepts like the distributive property and no-solution cases. Suitable for students in Grades 7-9.

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