Final answer:
The solution to the compound inequality in interval notation results in two separate intervals: (-∞,1) for the first inequality, and (-9,+∞) for the second. None of the provided choices accurately reflects these solutions, indicating a possible error or typo in the options given.
Step-by-step explanation:
The student has asked for the solution to a compound inequality in interval notation. The inequality is split into two separate inequalities: 5 - 2x > 3 and 7x + 8 > -55. To solve these inequalities:
- For the first inequality, 5 - 2x > 3, subtract 5 from both sides to get -2x > -2, and then divide by -2, remembering to reverse the inequality sign, yielding x < 1.
- For the second inequality, 7x + 8 > -55, subtract 8 from both sides to give 7x > -63, and then divide by 7 to find x > -9.
The solutions to these inequalities do not intersect, as there is no single x-value that satisfies both conditions. In interval notation, we have two separate intervals: (-∞,1) for the first inequality and (-9,+∞) for the second. Therefore, answer choice a, (-∞,-33)∪(18.5,+∞), appears to be incorrect, as is choice b and d. It seems we have a discrepancy with the given options, as none of them match the correct intervals we found. Thus, the provided options may contain an error or typo. It's essential to recheck the calculations and the options provided for the accurate interval notation.