Question

Which set expresses the solution to the compound inequality −2 ≤ 2x+1/3 − 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:−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: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}

Answer 1

Just choose a, b, c, or d

Answer 2

To solve the compound inequality \(-2 \leq \frac{2x+1}{3} - 4 < 1\), we can break it up into two separate inequalities.

1. **First Inequality:**
\[
-2 \leq \frac{2x+1}{3} - 4
\]
Adding 4 to both sides gives:
\[
2 \leq \frac{2x+1}{3}
\]
Multiplying both sides by 3 results in:
\[
6 \leq 2x + 1
\]
Subtracting 1 from both sides yields:
\[
5 \leq 2x
\]
Dividing by 2 gives:
\[
\frac{5}{2} \leq x
\]
or equivalently:
\[
x \geq \frac{5}{2}
\]

2. **Second Inequality:**
\[
\frac{2x+1}{3} - 4 < 1
\]
Adding 4 to both sides results in:
\[
\frac{2x+1}{3} < 5
\]
Multiplying both sides by 3 gives:
\[
2x + 1 < 15
\]
Subtracting 1 from both sides yields:
\[
2x < 14
\]
Dividing by 2 gives:
\[
x < 7
\]

Now, combining these results from both inequalities, we have:
\[
\frac{5}{2} \leq x < 7
\]

Thus, the solution expressed in set notation is:
\[
\{x : \frac{5}{2} \leq x < 7\}
\]

Therefore, the correct response is:
\(\{x: \frac{5}{2} \leq x < 7\}\)

Answer 3

The correct answer is **a**: \(\{x: \frac{5}{2} \leq x < 7\}\).