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.