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

Question

−
2
≤
2
𝑥
+
1
3
−
4
<
1
?(1 point)
Responses

{x:52≤x<1}
{
𝑥
:
5
2
≤
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}
{
𝑥
:
3
≤
𝑥
<
7
}
left brace x colon 3 less-than-or-equal-to x less than 7 right brace

{x:52≤x<7}
{
𝑥
:
5
2
≤
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:−32≤x<1}
{
𝑥
:
−
3
2
≤
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 \(-2 \leq 2x + 13 - 4 < 1\), let's first simplify the expression in the middle:

1. Combine like terms inside the inequality: \[-2 \leq 2x + 9 < 1\]

Now, we can break this compound inequality into two separate inequalities and solve each:

First inequality: \[ -2 \leq 2x + 9 \] Subtract 9 from both sides: \[ -2 - 9 \leq 2x \] \[ -11 \leq 2x \] Now, divide by 2: \[ -\frac{11}{2} \leq x \]

Second inequality: \[ 2x + 9 < 1 \] Subtract 9 from both sides: \[ 2x < 1 - 9 \] \[ 2x < -8 \] Now, divide by 2: \[ x < -4 \]

Now combine the two results: \[ -\frac{11}{2} \leq x < -4 \]

Converting \(-\frac{11}{2}\) to a decimal gives \(-5.5\). So the solution can be expressed as:

\[ -\frac{11}{2} \leq x < -4 \]

Now, we check which of the response sets this corresponds to:

1. \({x : \frac{5}{2} \leq x < 1}\) (not correct)
2. \({x : 3 \leq x < 7}\) (not correct)
3. \({x : \frac{5}{2} \leq x < 7}\) (not correct)
4. \({x : -\frac{3}{2} \leq x < 1}\) (not correct)

None of the options directly list the actual result of \(-\frac{11}{2} \leq x < -4\).

Since none of the provided options correspond to the correct inequality solution, it appears there is no accurate option given. The closest approximation or correct interpretation based on provided results does not appear to be present.

If you have more context or other options, please provide them for further assistance!