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:3≤x<7} left brace x colon 3 less-than-or-equal-to x less than 7 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

Answer 1

To solve the compound inequality \(-2 \leq 2x + 13 - 4 < 1\), we can break it down into two separate inequalities:

1. \(-2 \leq 2x + 13 - 4\)
2. \(2x + 13 - 4 < 1\)

Let's solve each inequality step by step.

### First Inequality:
\[
-2 \leq 2x + 13 - 4
\]
This simplifies to:
\[
-2 \leq 2x + 9
\]
Subtract 9 from both sides:
\[
-2 - 9 \leq 2x
\]
\[
-11 \leq 2x
\]
Now, divide both sides by 2:
\[
-\frac{11}{2} \leq x
\]

### Second Inequality:
\[
2x + 13 - 4 < 1
\]
This simplifies to:
\[
2x + 9 < 1
\]
Subtract 9 from both sides:
\[
2x < 1 - 9
\]
\[
2x < -8
\]
Now, divide both sides by 2:
\[
x < -4
\]

### Combining the Results:
So we have the combined inequalities:
\[
-\frac{11}{2} \leq x < -4
\]
Now, \(-\frac{11}{2} = -5.5\) and \(-4\) is a larger number. Therefore, \(x\) must satisfy:
\[
-\frac{11}{2} \leq x < -4
\]
This signifies \(x\) can be any value between -5.5 and -4, including -5.5 but not including -4.

### Set Representation:
The set notation for this solution would appear as:
\[
\{ x : -\frac{11}{2} \leq x < -4 \}
\]

### Conclusion:
Since none of the provided options perfectly matches this exact interval, you might want to check if any of the options can approximate or identify this interval, but based on the calculations, it should look more like \(-5.5 \leq x < -4\). If you want exact options based on choices, it looks like those could be scrutinized for approximation towards boundaries.

In short, let's ensure by checking:
1. No options given match -5.5 or -4 exactly.
2. Any shakedown intervals prompt checking options against receipts provided for double-verification.

Since actual values fall outside {5/2-5, directly assess conditions directly toward resolving overlaps only if the limit shifts toward common approximates captured.}