Question

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

Answer 1

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

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

\[
2x + 1 = -5
\]

Subtract 1 from both sides:

\[
2x = -5 - 1
\]
\[
2x = -6
\]

Now, divide by 2:

\[
x = -3
\]

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

\[
x - 1 > -4
\]

Add 1 to both sides:

\[
x > -4 + 1
\]
\[
x > -3
\]

**Final Solution Set:**

Now we combine the results:

- From the first equation, we have \(x = -3\).
- From the second inequality, we have \(x > -3\).

Since the problem states it is an "or" condition, the solution set includes all values of \(x\) that satisfy either equation. Thus, the solution set is:

\[
x \in (-3, \infty)
\]

This means \(x\) can take any value greater than \(-3\) or can also be exactly \(-3\). Therefore, we should explicitly include \(-3\):

\[
x \in [-3, \infty)
\]

This is the complete solution set.