Question

error analysis describe and correct the error in determining if 8 is in the solution set of the inequality. -y + 7 < -4 -8 + 7 <? -4 -1 < -4 8 is in the solution set. the simplification and the conclusion are both incorrect. the expression on the left simplifies to 1. since 1 is not less than -4, this means 8 is not in the solution set. the simplification is correct, but the conclusion is incorrect. the expression on the left simplifies to -1. since -1 is not less than -4, this means 8 is not in the solution set. the simplification is incorrect, but the conclusion is correct. because y is negative, the expression on the left simplifies to -15. since -15 is less than -4, this means 8 is in the solution set.

Explanation:

Step1: Analyze the error in logic

The error is in the simplification and comparison logic. When simplifying an inequality -y + 7 < - 4, we should first isolate y. Subtracting 7 from both sides gives -y < -11, then multiplying both sides by - 1 (and reversing the inequality sign) gives y>11. We can't just make incorrect simplifications like assuming the left - hand side simplifies to some wrong values (-1, 15 etc.) as in the error analysis.

Step2: Correct way to check if 8 is in the solution set

Substitute y = 8 into the original inequality -y + 7 < - 4. We get -(8)+7=-1, and -1 is not less than - 4. So 8 is not in the solution set.

Answer:

The error in the original analysis is incorrect simplification of the left - hand side of the inequality. To correctly determine if 8 is in the solution set, substitute 8 into the original inequality -y + 7 < - 4. Since -8 + 7=-1 and -1 is not less than - 4, 8 is not in the solution set.