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 negative 3 right brace

{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.

Answer 1

To solve the given inequalities and equation, we start with each part separately:

1. **For the equation \( 2x + 1 = -5 \):**
\[
2x + 1 = -5
\]
Subtracting 1 from both sides:
\[
2x = -6
\]
Dividing by 2:
\[
x = -3
\]

2. **For the inequality \( x - 1 > -4 \):**
\[
x - 1 > -4
\]
Adding 1 to both sides:
\[
x > -3
\]

Now, we combine the results. The equation gives us the specific solution \( x = -3 \), and the inequality gives us the solution set \( x > -3 \).

Since we are looking for the union of the two solution sets, we note that \( x = -3 \) is included in the set \( x > -3 \).

Thus, the complete solution set is:
\[
\{x \mid x \geq -3\}
\]

So, the correct response is:
\[
\{x \mid x \geq -3\}
\]