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

Responses

{x:52≤x<7}
{x:52≤x<7}
- not selected, this is the correct answer

{x:3≤x<7}
{x:3≤x<7}
- no response given

{x:−32≤x<1}
{x:−32≤x<1}
- incorrect

{x:52≤x<1} in 2 sentences tell me why it is correct

1 answer

The correct set that expresses the solution to the compound inequality \(-2 \leq 2x + 13 - 4 < 1\) is \({x: 5/2 \leq x < 7}\). This is because, when the inequality is simplified and solved step by step, it results in the values of \(x\) being bounded between \(\frac{5}{2}\) (or 2.5) and 7.