https://file.aiquickdraw.com/mathbot/file/1727117204708sziwlg7y.jpg

The given equation is:

\[
10 + |m - 6| = 7
\]

Let's solve it step-by-step:

### Step 1: Isolate the absolute value expression
Subtract 10 from both sides:
\[
|m - 6| = 7 - 10
\]
\[
|m - 6| = -3
\]

### Step 2: Analyze the result
Since the absolute value of any real number is always non-negative, \(|m - 6| = -3\) has no solution in real numbers.

### Conclusion
There is **no real solution** to the equation.

Would you like more details or have any questions?

### 5 Related Questions
1. How do we handle absolute value equations in general?
2. Can there be any scenario where an absolute value equation has no solution?
3. What happens when an absolute value equation has multiple solutions?
4. How do we solve an inequality involving absolute values, such as \(|x - 3| > 5\)?
5. What does the graph of an absolute value function look like?

### Tip
Always check the sign of the expression on the right side of the equation when solving absolute value equations. If it's negative, there is no real solution!

Learn how to solve the absolute value equation 10 + |m - 6| = 7. This problem involves isolating the absolute value and analyzing the solution based on algebraic principles. Suitable for students in Grades 8-10.

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