Question

Which set expresses the solution to the compound inequality −3≤2x−5<1 ? Responses {x:3.5≤x<5.5} {x:3.5≤x<5.5} - no response given {x | 2≤x<6} {x | 2≤x<6} - no response given {x:1≤x<3} {x:1≤x<3} - no response given {x | −1.5≤x<0.5} {x | −1.5≤x<0.5} - no response given

Answer 1

To solve the compound inequality \(-3 \leq 2x - 5 < 1\), we can break it into two parts and solve for \(x\).

1. **Solving \(-3 \leq 2x - 5\):**

\[
-3 + 5 \leq 2x
\]
\[
2 \leq 2x
\]
\[
1 \leq x
\]
or
\[
x \geq 1
\]

2. **Solving \(2x - 5 < 1\):**

\[
2x - 5 < 1
\]
\[
2x < 1 + 5
\]
\[
2x < 6
\]
\[
x < 3
\]

Combining both parts of the inequality, we have:

\[
1 \leq x < 3
\]

In set notation, this can be expressed as:

\[
\{x | 1 \leq x < 3\}
\]

So among your given options, the correct set expressing the solution to the compound inequality \(-3 \leq 2x - 5 < 1\) is:

\({x:1 \leq x < 3}\)