The equation given is \( |w| = 6 \), which is an absolute value equation. Here's how to solve it step by step:

### Step 1: Understand the absolute value concept
The absolute value of a number represents its distance from zero on the number line, regardless of direction. This means:
\[
|w| = 6
\]
implies that \( w \) could either be 6 or \(-6\), since both \( 6 \) and \( -6 \) are exactly 6 units away from zero.

### Step 2: Set up two equations
From the property of absolute value:
\[
w = 6 \quad \text{or} \quad w = -6
\]
Thus, the solution is \( w = 6 \) or \( w = -6 \).

### Step 3: Graphing the solution
On the number line, plot points at \( w = 6 \) and \( w = -6 \). These two points represent the possible values of \( w \).

### Explanation
1. The absolute value equation \( |w| = 6 \) gives two possible values for \( w \) because both positive and negative values can have the same absolute value.
2. This solution can be graphed as two distinct points on the number line, located at \( w = 6 \) and \( w = -6 \).

### Visual Representation
On a number line:
- Place a point at \( w = -6 \) on the left of zero.
- Place a point at \( w = 6 \) on the right of zero.

### Summary
The solution to \( |w| = 6 \) is:
\[
w = 6 \quad \text{or} \quad w = -6
\]
On a graph, these values are represented as two points: \( w = -6 \) and \( w = 6 \) on the number line.

Would you like me to provide a graphical representation or further explanation?

Here are 5 related questions to explore:

1. How would you solve the equation \( |x - 3| = 7 \)?
2. What happens when the absolute value equation has no solution, like \( |y| = -5 \)?
3. How can absolute value inequalities be solved, such as \( |z| < 4 \)?
4. How do we interpret \( |w| = 0 \)?
5. Can we graph absolute value functions, such as \( y = |x| \)?

**Tip**: When solving absolute value equations, always remember to set up two equations: one for the positive case and one for the negative case.

Learn how to solve the absolute value equation |w| = 6 with a detailed step-by-step guide. Understand the concept of absolute value, set up equations, and graph the solutions effectively. Suitable for students in Grades 7-9.

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