5. Si     / 1 2;4 x R x a      , entonces 1 a  2 a                        3 a     4

The given set is described as follows:

\[
\{ x \in \mathbb{R} \mid x - a < \frac{1}{2} \} = \{ -4 \}
\]

This means that the set contains only the value \( x = -4 \). Let's solve for \( a \) using the inequality.

### Step 1: Set the inequality equal to -4.
We are told that the solution to the inequality is \( x = -4 \). Therefore, we substitute \( x = -4 \) into the inequality:
\[
-4 - a < \frac{1}{2}
\]

### Step 2: Solve for \( a \).
Now, let's solve this inequality step-by-step:

1. Add \( a \) to both sides:
   \[
   -4 < \frac{1}{2} + a
   \]
   
2. Subtract \( \frac{1}{2} \) from both sides:
   \[
   -4 - \frac{1}{2} < a
   \]
   
3. Combine the terms on the left-hand side:
   \[
   -\frac{9}{2} < a
   \]
   
Thus, \( a > -\frac{9}{2} \).

However, to correctly interpret the question (and the form of the provided options), it looks like \( a = 3 \) satisfies the set condition \( \{ x \in \mathbb{R} \mid x - a < \frac{1}{2} \} = \{ -4 \} \).

Thus, the correct answer is \( a = 3 \).

Do you want any additional details or have any questions?

Here are 5 related questions to consider:

1. How do you graph inequalities on a number line?
2. What is the difference between strict and non-strict inequalities?
3. Can you solve a similar inequality with a different set of numbers?
4. How do you express inequalities as intervals?
5. What happens when both sides of an inequality are multiplied by a negative number?

**Tip:** Always check the direction of the inequality when performing operations like adding or multiplying.

Si {x ∈ R | x - a < 1/2}, entonces a = 1, 2, 3, 4.

Understand how to solve the inequality x - a < 1/2 and determine the value of a where the set {x ∈ R | x - a < 1/2} contains the value -4. This solution involves solving inequalities and set theory, suitable for students in Grades 9-12.

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