Questions: Write the set x x ≠ -4 using interval notation

Transcript text: Question 7 Write the set $\{x \mid x \neq-4\}$ using interval notation

Solution

Solution Steps

To express the set $\{x \mid x \neq -4\}$ in interval notation, we need to represent all real numbers except $-4$. This can be done by combining two intervals: one that includes all numbers less than $-4$ and another that includes all numbers greater than $-4$.

Step 1: Understanding the Set

The set $\{x \mid x \neq -4\}$ includes all real numbers except $-4$. This means we need to express this set in a way that covers all numbers less than $-4$ and all numbers greater than $-4$.

Step 2: Expressing the Set in Interval Notation

To express the set in interval notation, we use two intervals:

The first interval $(- \infty, -4)$ represents all numbers less than $-4$.
The second interval $(-4, \infty)$ represents all numbers greater than $-4$.

Step 3: Combining the Intervals

The union of these two intervals gives us the complete set of all real numbers except $-4$. In interval notation, this is written as: \[ (-\infty, -4) \cup (-4, \infty) \]

Final Answer

$\boxed{(-\infty, -4) \cup (-4, \infty)}$

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