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The equation shown is:

\[
|5x| = 10
\]

To solve this absolute value equation, we consider two cases:

1. **Case 1**: \( 5x = 10 \)
   \[
   x = \frac{10}{5} = 2
   \]

2. **Case 2**: \( 5x = -10 \)
   \[
   x = \frac{-10}{5} = -2
   \]

Thus, the solutions to the equation \( |5x| = 10 \) are:

\[
x = 2 \quad \text{or} \quad x = -2
\]

Would you like more details or clarifications?

Here are 5 related questions for further exploration:

1. What are the steps to solve general absolute value equations?
2. How do we graph the function \( y = |5x| \)?
3. What happens if the absolute value equation has no solution?
4. How would the solutions change if the equation were \( |5x + 3| = 10 \)?
5. Can you explain how to solve absolute value inequalities?

**Tip:** When solving absolute value equations, always break it down into two cases: one for the positive expression and one for the negative expression inside the absolute value.

Explore how to solve the absolute value equation |5x| = 10. This problem introduces the key concepts of absolute value equations, with a step-by-step guide breaking it down into two cases: positive and negative values inside the absolute value. Ideal for students in Grades 7-9.

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