Final answer:
To find the smallest integer in the solution set for the inequality 3 ≤ 2x-3<15, we solve for x to obtain 3 ≤ x < 9. The smallest integer that fulfills this condition is 3.
Step-by-step explanation:
The student's question asks: What is the value of the smallest integer in the solution set for 3 ≤ 2x-3<15? To solve for the variable x, we'll first isolate it in the inequality.
- Add 3 to all sides of the inequality: 3 + 3 ≤ 2x - 3 + 3 < 15 + 3, which simplifies to 6 ≤ 2x < 18.
- Divide all parts by 2 to solve for x: 6/2 ≤ x < 18/2, resulting in 3 ≤ x < 9.
Now we need to find the smallest integer that is greater than or equal to 3. The answer is simply 3, since it is the smallest integer that satisfies the inequality 3 ≤ x.