Question

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

A) {x|x>−3}
start set x such that x is greater than negative 3 end set - incorrect

B) {x|x≥−3}
start set x such that x is greater than or equal to negative 3 end set - no response given

C) {−3}
start set negative 3 end set - no response given

D) The solution set is null.

Answer 1

To find the solution set for the expression \(2x + 1 = -5\) or \(x - 1 > -4\), we will solve each equation separately.

1. **Solve the equation \(2x + 1 = -5\):**
- Subtract 1 from both sides:
\[
2x = -5 - 1 \Rightarrow 2x = -6
\]
- Divide by 2:
\[
x = -3
\]

2. **Solve the inequality \(x - 1 > -4\):**
- Add 1 to both sides:
\[
x > -4 + 1 \Rightarrow x > -3
\]

Now, we combine the solutions:

- The equation gives a solution of \(x = -3\).
- The inequality gives the solution set \(x > -3\).

Therefore, the overall solution set is the combination of both results:

- \(x = -3\) is included, and \(x > -3\) means all numbers greater than \(-3\) are also included.

Thus, the solution set can be expressed as:

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

This corresponds to Response **B**: \(\{x | x \geq -3\}\).

So the correct answer is **B**.