Question

Which set expresses the solution to the compound inequality −2≤2x+13−4<1
?(1 point)
Responses

{x: −32≤x<1}
{x: −32≤x<1}

{x: 52≤x<1}
{x: 52≤x<1}

{x: 52≤x<7}

Answer 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 \([-5.5 \leq x < -4]\).