Which set expresses the solution to the compound inequality −3≤2x−5<1

Question

?(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:

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