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Let's solve each of the given equations one by one.

### (a) \(\left| a + 5 \right| = 3\)
For an absolute value equation like \(\left| a + 5 \right| = 3\), we have two cases to solve:

1. \(a + 5 = 3\)
   \[
   a = 3 - 5 = -2
   \]

2. \(a + 5 = -3\)
   \[
   a = -3 - 5 = -8
   \]

So, the solution set for part (a) is \(a = -2\) and \(a = -8\).

### (b) \(\left| a + 5 \right| = 0\)
The absolute value of any expression is zero only if the expression itself is zero. Therefore:

\[
a + 5 = 0
\]
\[
a = -5
\]

So, the solution set for part (b) is \(a = -5\).

### (c) \(\left| a + 5 \right| = -2\)
An absolute value cannot be negative, so there are **no solutions** for this equation.

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### Summary of Solutions:
- (a) \(a = -2, -8\)
- (b) \(a = -5\)
- (c) No solution

Would you like further details on any step? Here are five related questions to expand on this:

1. What are the properties of absolute value equations?
2. How can absolute value inequalities be solved?
3. Can absolute value equations have no solutions, and why?
4. How do you graph absolute value functions?
5. What is the geometric interpretation of an absolute value equation?

**Tip**: When solving absolute value equations, always remember to check for both the positive and negative cases!

Solve the equations: (a) |a + 5| = 3, (b) |a + 5| = 0, (c) |a + 5| = -2

Learn how to solve the absolute value equations |a + 5| = 3, |a + 5| = 0, and |a + 5| = -2. This step-by-step solution covers key concepts, including absolute value properties and how to solve linear equations. Suitable for students in Grades 6-8.

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