Question

Find the solution set of 2x+1=−5
or x−1>−4
.(1 point)
Responses

{x|x≥−3}
left brace x vertical bar x greater-than-or-equal-to negative 3 right brace

{−3}
left brace negative 3 right brace

The solution set is null.
The solution set is null.

{x|x>−3}

Answer 1

To find the solution set of the compound inequality \(2x + 1 = -5\) or \(x - 1 > -4\), we will solve each part separately.

1. **Solving \(2x + 1 = -5\):**

\[
2x + 1 = -5
\]
Subtract 1 from both sides:
\[
2x = -6
\]
Divide both sides by 2:
\[
x = -3
\]

2. **Solving \(x - 1 > -4\):**

\[
x - 1 > -4
\]
Add 1 to both sides:
\[
x > -3
\]

Now, we combine the results:

- From \(2x + 1 = -5\), we found \(x = -3\).
- From \(x - 1 > -4\), we found \(x > -3\).

Since the compound statement is connected by "or", the solution set includes any \(x\) that satisfies either part of the equation. Therefore, the solution set can be expressed as:

\[
x \geq -3 \quad \text{(since } x = -3 \text{ also satisfies the inequality } x > -3\text{)}
\]

Thus, the solution set is:

\[
\{ x \mid x \geq -3 \}
\]

So the correct response is:

**\(\{ x \mid x \geq -3 \}\)**.