Question

Which set expresses the solution to the compound inequality −3≤2x−5<1
?(2 points)
Responses

{x:1≤x<3}
{x:1≤x<3}

{x | 2≤x<6}
{x | 2≤x<6}

{x:3.5≤x<5.5}
{x:3.5≤x<5.5}

{x | −1.5≤x<0.5}

Answer 1

To solve the compound inequality \(-3 \leq 2x - 5 < 1\), we will tackle it in two parts.

1. **Solve the left part:**
\(-3 \leq 2x - 5\)

Add 5 to both sides:
\[
2 \leq 2x
\]

Divide by 2:
\[
1 \leq x \quad \text{or} \quad x \geq 1
\]

2. **Solve the right part:**
\(2x - 5 < 1\)

Add 5 to both sides:
\[
2x < 6
\]

Divide by 2:
\[
x < 3
\]

Now we combine these two results:

\[
1 \leq x < 3
\]

In set notation, this is expressed as:

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

So the correct response is:

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