Explanation:
No, Richard's inequality is not correct. In order to determine the correct inequality, we first need to find the total number of books that Richard read in 4th and 5th grade. In 5th grade, he read 9 more books than in 4th grade, so the total number of books he read in 5th grade was 37 + 9 = 46 books. The total number of books he read in 4th and 5th grade is therefore 46 + 37 = 83 books.
Since Richard plans to read at least 12 more books than the total number of books he read in 4th and 5th grade, he needs to read at least 83 + 12 = 95 books in 6th grade. In order to have read at least 180 books in total over 4th, 5th, and 6th grade, his inequality should be b ≥ 180. However, b represents the number of books he plans to read in 6th grade, which means the inequality should be 95 ≥ 180, which is not true. Therefore, Richard's inequality is not correct.