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

Question

?

Answer 1

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 2

{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 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!