Final answer:
a)The correct solution for the inequality −10 ≤ 2x − 20 ≤ 30 is 5 ≤ x ≤ 25. However, this does not match any of the provided options, suggesting there may be a typo or an error in the question or options.
Step-by-step explanation:
The correct answer is option A. To solve the compound inequality −10 ≤ 2x − 20 ≤ 30, we first add 20 to all parts of the inequality:
- −10 + 20 ≤ 2x − 20 + 20 ≤ 30 + 20
- 10 ≤ 2x ≤ 50
Next, we divide the entire inequality by 2 to solve for x:
- 10 / 2 ≤ 2x / 2 ≤ 50 / 2
- 5 ≤ x ≤ 25
However, this solution does not match any of the given options. This suggests that there may have been a typo in the original question or the options provided.
If the options reflect the correct intervals for x, then none of the options given would be the solution to the inequality provided. In such cases, it is advisable to revisit the question and the options or consult with the instructor for clarification.