https://file.aiquickdraw.com/mathbot/file/1727070032246rjr9jr9t.jpg

The given equation is:

\[
|y + 3| = 17
\]

To solve this absolute value equation, we need to consider two cases, as the absolute value of a number is always non-negative and represents the distance from zero. The general approach is to split the equation into two parts:

### Case 1:
\[
y + 3 = 17
\]

Solving for \( y \):
\[
y = 17 - 3
\]
\[
y = 14
\]

### Case 2:
\[
y + 3 = -17
\]

Solving for \( y \):
\[
y = -17 - 3
\]
\[
y = -20
\]

### Final Answer:
The solutions are \( y = 14 \) and \( y = -20 \).

Would you like further details on how this method works? Feel free to ask any clarifying questions.

Here are 5 related questions to explore:

1. What are the steps to solve general absolute value equations?
2. How do we solve inequalities involving absolute values?
3. What are some real-life applications of absolute value functions?
4. How do absolute value functions behave graphically?
5. Can an absolute value equation have no solution?

**Tip:** When solving absolute value equations, always consider both the positive and negative cases!

Learn how to solve the absolute value equation |y + 3| = 17 step by step. This problem covers key algebraic concepts, including handling absolute values and solving for variables. Suitable for students in Grades 7-9.

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