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

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

{−3}
left brace negative 3 right brace

{x|x>−3}

Answer 1

To solve the system of inequalities and equations you provided, we have:

1. \( 2x + 1 = -5 \)
2. \( x - 1 > -4 \)

Let's solve each part separately:

1. For the equation \( 2x + 1 = -5 \):
\[
2x = -5 - 1
\]
\[
2x = -6
\]
\[
x = -3
\]

2. For the inequality \( x - 1 > -4 \):
\[
x > -4 + 1
\]
\[
x > -3
\]

Now let's combine the results from both parts:

- The solution to the equation is \( x = -3 \).
- The solution to the inequality is \( x > -3 \).

Thus, the overall solution set includes:

1. The point \( x = -3 \) from the equation, and
2. All the points greater than \(-3\) from the inequality.

In interval notation, this means the solution set can be expressed as:

\[
x \geq -3
\]

In set notation, this is represented as:

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

Therefore, the correct response is:

\(\{x | x \geq -3\}\)