https://file.aiquickdraw.com/mathbot/file/1726193626091izm3e3eo.jpg

The equation given in the image is:

\[
10 - 4(3 - 2y) = 8y - 5
\]

Let's solve this step by step:

### Step 1: Distribute the \(-4\) over the terms inside the parentheses:
\[
10 - 4 \cdot 3 + 4 \cdot 2y = 8y - 5
\]
\[
10 - 12 + 8y = 8y - 5
\]

### Step 2: Simplify the left side:
\[
-2 + 8y = 8y - 5
\]

### Step 3: Subtract \(8y\) from both sides to eliminate the \(8y\) term:
\[
-2 = -5
\]

This results in a contradiction, since \(-2\) does not equal \(-5\). This means that there is **no solution** to this equation. The equation is inconsistent.

Would you like more details on this process or any other questions related to solving equations? Here are some related questions to expand on this topic:

1. What is a contradiction in algebraic equations, and why does it lead to no solution?
2. Can you explain the steps for solving linear equations in more detail?
3. How would the equation change if we altered the constants?
4. What does it mean when an equation has infinitely many solutions?
5. How do systems of equations relate to this kind of algebraic problem?

**Tip**: When solving equations, always check for contradictions or identical terms on both sides to identify whether an equation has no solution or infinite solutions.

Learn how to solve the linear equation 10 - 4(3 - 2y) = 8y - 5. This problem covers key algebraic concepts such as the distributive property and understanding contradictions in equations. Suitable for students in Grades 7-9.

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