||13y+9||+8=2 give me whole number answer

Let's solve the equation \( ||13y + 9|| + 8 = 2 \), where \( || \cdot || \) denotes the absolute value.

### Step 1: Isolate the absolute value expression.
Subtract 8 from both sides to isolate the absolute value:

\[
||13y + 9|| = 2 - 8
\]
\[
||13y + 9|| = -6
\]

### Step 2: Analyze the equation.
The absolute value of any expression is always non-negative (i.e., \( || \cdot || \geq 0 \)). Since we have \( ||13y + 9|| = -6 \), and \(-6\) is negative, there is no solution to this equation.

### Conclusion:
There is no whole number (or any real number) solution for this equation.

Would you like more details or have any further questions?

### Related Questions:
1. What if the equation was \( ||13y + 9|| + 8 = 10 \)?
2. How would you solve \( |13y + 9| = 6 \)?
3. What is the difference between absolute value equations and inequalities?
4. How do you solve \( ||ax + b|| = c \) in general?
5. What happens if you remove the absolute value from the equation?
6. How would you solve \( ||13y + 9|| - 8 = 2 \)?
7. What if the equation was \( ||13y + 9|| + 8 = -10 \)?
8. What does it mean graphically when the absolute value equals a negative number?

### Tip:
Always remember that the absolute value of an expression cannot be negative, which helps quickly identify if an equation has no solution.

Learn how to solve the absolute value equation ||13y + 9|| + 8 = 2 with a detailed step-by-step solution. Understand why this equation has no whole number (or any real number) solution. Suitable for students in Grades 7-9.

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