Question

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

{x:52≤x<7}
left brace x colon Start Fraction 5 over 2 End Fraction less-than-or-equal-to x less than 7 right brace

{x:52≤x<1}
left brace x colon Start Fraction 5 over 2 End Fraction less-than-or-equal-to x less than 1 right brace

{x:−32≤x<1}
left brace x colon Start Fraction negative 3 over 2 End Fraction less-than-or-equal-to x less than 1 right brace

{x:3≤x<7}

Answer 1

if your answer isn't a answer on the options, your answer isn't correct

Answer 2

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

1. Combine constants:
\[
-2 \leq 2x + 9 < 1
\]

Next, we break this into two separate inequalities to solve:

### First Inequality:
\[
-2 \leq 2x + 9
\]

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

Now, divide by 2:
\[
-\frac{11}{2} \leq x \quad \text{or} \quad x \geq -\frac{11}{2}
\]

### Second Inequality:
\[
2x + 9 < 1
\]

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

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

### Combining the Results:
We have two results:
1. \(x \geq -\frac{11}{2}\) (this is approximately -5.5)
2. \(x < -4\)

Combining these, we find:
\[
-\frac{11}{2} \leq x < -4
\]

Now, let's check what this expression means.
This means \(x\) can take values between \(-5.5\) and \(-4\) (not including -4). However, let’s put it into the options provided.

Now, converting \(-\frac{11}{2}\) to decimal gives:
\[
-\frac{11}{2} = -5.5
\]

This allows us to express the solution set formally as:
\[
\{ x \mid -\frac{11}{2} \leq x < -4 \}
\]

Now, looking at the options you've provided, there does not appear to be a direct match, but based on calculations, we can check if one of the expressions could represent this set.

If I just check the options:
- **None of the offered choices exactly contain \(-\frac{11}{2}\)**.
- Still, the closest representation would lead to checking if any of these options represent \(-\frac{11}{2}\).

However, since there are no matches listed, it suggests that there might be a reviewing of options required or misplacement in the problem or answers given.

If we made a mistake at a different point, let’s review.

In the absence of available correct matches, **none of the provided options seem correct** for the final solution to the given compound inequality based on \(x\) values between \(-5.5\) and \( -4\).

Thus, claim your final output was:
\(\{x: -\frac{11}{2} \leq x < -4 \}\), which isn't represented in the options directly stated. Would you like further clarification or assistance?

Answer 3

I apologize for the confusion and appreciate your understanding. Let's go through the compound inequality step by step again and ensure we can find an accurate solution that matches one of the provided options.

The original inequality is:

\[
-2 \leq 2x + 13 - 4 < 1
\]

### Step 1: Simplify the Inequality

Combine like terms:
\[
-2 \leq 2x + 9 < 1
\]

### Step 2: Split Into Two Inequalities

We can tackle the inequalities separately:

1. **First Inequality:**
\[
-2 \leq 2x + 9
\]

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

Now divide by 2:
\[
-\frac{11}{2} \leq x \quad \text{or} \quad x \geq -\frac{11}{2}
\]

2. **Second Inequality:**
\[
2x + 9 < 1
\]

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

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

### Step 3: Combine the Results

From the inequalities, we have:
\[
-\frac{11}{2} \leq x < -4
\]

Now converting \(-\frac{11}{2}\) to decimal gives:
\[
-\frac{11}{2} = -5.5
\]

So the combined solution is:
\[
-\frac{11}{2} \leq x < -4 \quad \text{or} \quad -5.5 \leq x < -4
\]

### Matching with Options

Now let’s check the options you've provided again:

1. **{x: \( \frac{5}{2} \leq x < 7 \)}**
2. **{x: \( \frac{5}{2} \leq x < 1 \)}**
3. **{x: \( -\frac{3}{2} \leq x < 1 \)}**
4. **{x: \( 3 \leq x < 7 \)}**

None of these options reflect the solution we obtained, \( -5.5 \leq x < -4\).

### Conclusion

It appears that none of the provided options are correct. Given the processes followed, it seems there's a discrepancy between the solution derived and those offered. If there's further clarification or additional information on the context, I’d be glad to help resolve it!