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Answer :
Final answer:
The solution to the inequality −7 < x − 1 < 8 is −6 < x < 9, which means x can be any number between -6 and 9, excluding -6 and 9 themselves.
Explanation:
The student has asked to solve the compound inequality −7 < x − 1 < 8. To solve for x, we need to isolate x in the middle of the inequality by performing the same operation on all three parts. Here's how to do it step-by-step:
- Add 1 to all three parts of the inequality to cancel out the -1 attached to x. This yields: −6 < x < 9.
- Now x is isolated, and we have our solution: x is greater than -6 and less than 9.
- Check the answer to see if it is reasonable. Since x is between two integer numbers, we can verify a few values within the range to ensure they satisfy the original inequality.
For example, if x were 0, substituting it into the original inequality gives us −7 < -1 < 8, which is true. Therefore, the solution set is: −6 < x < 9.
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