Rewrite the following equation in standard form and determine if there is a solution.

||||12x−33||||+8=3


To rewrite the equation \( ||12x - 33|| + 8 = 3 \) in standard form and determine if there is a solution, let's follow these steps:

### Step 1: Isolate the absolute value expression
First, subtract 8 from both sides of the equation:
\[
||12x - 33|| + 8 = 3
\]
\[
||12x - 33|| = 3 - 8
\]
\[
||12x - 33|| = -5
\]

### Step 2: Analyze the result
The absolute value of any expression is always non-negative. Therefore, \( ||12x - 33|| \) cannot be equal to a negative number like \(-5\).

### Conclusion:
Since an absolute value cannot be negative, there is **no solution** to this equation.

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Would you like further clarification on this? Here are some related questions for practice:

1. How do you solve absolute value equations when the right-hand side is positive?
2. What happens when you solve \( ||ax + b|| = 0 \)?
3. How do absolute value inequalities differ from equations?
4. What is the graph of \( ||ax + b|| \) and how does it help in finding solutions?
5. How do absolute value functions affect both sides of the number line?

**Tip:** Always check whether an absolute value equation has a non-negative right-hand side before solving!

Rewrite the following equation in standard form and determine if there is a solution.

||||12x−33||||+8=3

Learn how to rewrite and solve the absolute value equation ||12x − 33|| + 8 = 3. This problem explores key algebraic concepts like absolute value properties and equations. Suitable for students in Grades 8-10.

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