Which set expresses the solution to the compound inequality −2≤2x+13−4<1

To solve the compound inequality \(-2 \leq 2x + 13 - 4 < 1\), we first simplify the middle part of the inequality:

1. Simplify \(2x + 13 - 4\): \[ 2x + 9 \]

So, the compound inequality becomes: \[ -2 \leq 2x + 9 < 1 \]

Now we will break this into two separate inequalities:

Step 1: Solve \(-2 \leq 2x + 9\)

Subtract \(9\) from both sides: \[ -2 - 9 \leq 2x \implies -11 \leq 2x \]

Now, divide by \(2\): \[ -5.5 \leq x \implies x \geq -5.5 \]

Step 2: Solve \(2x + 9 < 1\)

Subtract \(9\) from both sides: \[ 2x < 1 - 9 \implies 2x < -8 \]

Now, divide by \(2\): \[ x < -4 \]

Step 3: Combine the results

We have: \[ -5.5 \leq x < -4 \]

This can be expressed in interval notation as: \[ [-5.5, -4) \]

Finding the correct response

If we examine the options provided:

1. \({x: -32 \leq x < 1}\)
2. \({x: 52 \leq x < 1}\)
3. \({x: 52 \leq x < 7}\)

None of these match the derived solution \([-5.5, -4)\). This suggests that there might be a miscommunication, typo, or error in the options listed.

If looking for a correct representation of the solution based on the findings, none of the options are correct as per the derived inequality results. Please double-check the options or provide correct options reflecting the solution \([-5.5 \leq x < -4]\).