Question

Which set expresses the solution to the compound inequality −3≤2x−5<1
?

Answer 1

{x | −1.5≤x<0.5}
{x | −1.5≤x<0.5}
- no response given

{x:3.5≤x<5.5}
{x:3.5≤x<5.5}
- no response given

{x:1≤x<3}
{x:1≤x<3}
- no response given

{x | 2≤x<6}

Answer 2

To solve the compound inequality \(-3 \leq 2x - 5 < 1\), we can break it down into two parts:

1. Solve \(-3 \leq 2x - 5\)
2. Solve \(2x - 5 < 1\)

### Step 1: Solve \(-3 \leq 2x - 5\)

Add 5 to both sides:

\[
-3 + 5 \leq 2x
\]
\[
2 \leq 2x
\]

Now, divide both sides by 2:

\[
1 \leq x \quad \text{or} \quad x \geq 1
\]

### Step 2: Solve \(2x - 5 < 1\)

Add 5 to both sides:

\[
2x < 1 + 5
\]
\[
2x < 6
\]

Now, divide both sides by 2:

\[
x < 3
\]

### Combine the Results

Now we combine the two parts of the compound inequality:

\[
1 \leq x < 3
\]

This can be expressed in interval notation as:

\[
[1, 3)
\]

### Conclusion

The solution to the compound inequality \(-3 \leq 2x - 5 < 1\) is:

\[
x \in [1, 3)
\]

Answer 3

It looks like you're listing several sets that represent intervals of values. I'll clarify what each of these sets means:

1. **Set: \(\{x \mid -1.5 \leq x < 0.5\}\)**
- This set includes all values of \(x\) such that \(x\) is greater than or equal to \(-1.5\) and less than \(0.5\). In interval notation, this can be represented as:
\[
[-1.5, 0.5)
\]

2. **Set: \(\{x \mid 3.5 \leq x < 5.5\}\)**
- This set includes all values of \(x\) such that \(x\) is greater than or equal to \(3.5\) and less than \(5.5\). In interval notation, this can be represented as:
\[
[3.5, 5.5)
\]

3. **Set: \(\{x \mid 1 \leq x < 3\}\)**
- This set includes all values of \(x\) such that \(x\) is greater than or equal to \(1\) and less than \(3\). In interval notation, this can be represented as:
\[
[1, 3)
\]

4. **Set: \(\{x \mid 2 \leq x < 6\}\)**
- This set includes all values of \(x\) such that \(x\) is greater than or equal to \(2\) and less than \(6\). In interval notation, this can be represented as:
\[
[2, 6)
\]

If you need further explanations or have additional questions about these sets, feel free to ask!