To analyze the statement, let’s examine the relationship between the two inequalities:

Given:
\[
|x + 2| < 0.3
\]
we need to show that this implies:
\[
|4x + 8| < 1.2
\]

### Step 1: Understanding the Implication
The key here is to rewrite \(|4x + 8|\) in terms of \(|x + 2|\). Notice that:
\[
4x + 8 = 4(x + 2)
\]
So, \(|4x + 8| = |4(x + 2)| = 4 |x + 2|\).

### Step 2: Substituting in the Inequality
Since \(|x + 2| < 0.3\), we can multiply both sides by 4:
\[
4 |x + 2| < 4 \cdot 0.3
\]
which simplifies to:
\[
|4x + 8| < 1.2
\]

Thus, the inequality \(|x + 2| < 0.3\) indeed implies that \(|4x + 8| < 1.2\), as required.

Let me know if you'd like further details or have any questions.

### Related Questions
1. How do we solve inequalities involving absolute values?
2. What other transformations can we apply to absolute value inequalities?
3. How would the result change if \(|x + 2| \leq 0.3\) instead of \(|x + 2| < 0.3\)?
4. What if the inequality was reversed, like \(|x + 2| > 0.3\)?
5. How do we handle absolute values when inequalities involve variables on both sides?

**Tip:** When working with absolute value inequalities, try rewriting the expression in simpler terms by factoring out constants if possible—it can make relationships clearer.

Understand how the inequality |x + 2| < 0.3 implies |4x + 8| < 1.2. This problem involves essential algebraic concepts like absolute value properties and inequality manipulation, suitable for students in Grades 9-11.

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