Find the solution set of 2x+1=−5

Question

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:

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