https://file.aiquickdraw.com/mathbot/file/1726808959739aa6p4i7b.jpg

The equation in the image appears to be:

\[
|r + 2| = 9.4
\]

To solve this equation, we need to consider the absolute value. The general rule for solving absolute value equations like \( |A| = B \) is to split it into two cases:

1. \( A = B \)
2. \( A = -B \)

So, applying this rule here:

### Case 1:
\[
r + 2 = 9.4
\]
Subtract 2 from both sides:
\[
r = 9.4 - 2 = 7.4
\]

### Case 2:
\[
r + 2 = -9.4
\]
Subtract 2 from both sides:
\[
r = -9.4 - 2 = -11.4
\]

Thus, the solutions are:
\[
r = 7.4 \quad \text{or} \quad r = -11.4
\]

Would you like further explanation, or do you have any questions? Here are five related questions:

1. How do we verify the solutions of absolute value equations?
2. What happens if the right side of the equation is negative in an absolute value equation?
3. Can we apply this method to solve more complex absolute value equations with variables on both sides?
4. What would happen if we squared both sides of the equation before solving?
5. Can we solve absolute value inequalities similarly?

**Tip**: Always check both cases in absolute value equations to ensure no solution is missed.

Learn how to solve the absolute value equation |r + 2| = 9.4 with step-by-step guidance. This algebra problem demonstrates how to break down absolute value equations into two cases, r + 2 = 9.4 and r + 2 = -9.4, and solve for both possible values of r. Suitable for students in Grades 6-8.

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