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.