Solve the following equations with absolute values in them.
`|0|=6`

Answer

To solve the equation involving absolute values, we start with the equation:

**Given Equation:**
\[ |a| = 6 \]

### Step 1: Understand the Definition of Absolute Value
The absolute value of a number \( a \) is defined as the distance of \( a \) from 0 on the number line, regardless of direction. This means:
\[ |a| = a \quad \text{if } a \geq 0 \]
\[ |a| = -a \quad \text{if } a < 0 \]

### Step 2: Set Up the Two Cases
From the definition of absolute value, we can derive two cases from the equation \( |a| = 6 \):
1. Case 1: \( a = 6 \)
2. Case 2: \( a = -6 \)

### Step 3: Solve Each Case
- For **Case 1**:
\[ a = 6 \]

- For **Case 2**:
\[ a = -6 \]

### Step 4: Write the Final Solutions
The solutions to the equation \( |a| = 6 \) are:
\[ a = 6 \quad \text{or} \quad a = -6 \]

### Conclusion
Thus, the final solution set is:
\[ a = 6 \text{ or } a = -6 \]

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