Answer:
A: line 3 to 4; distributive property was incorrectly applied
B: line 8 to 9: division by a negative number was incorrect
Step-by-step explanation:
You want to know where errors occurred in the solution of the given inequality, and what the errors were.
A. First error
The first error occurred going from line 3 to line 4.
Expressions 2(x -2) and 3(x -4) were incorrectly evaluated as 2x-2 and 3x-4. The distributive property requires the factor to be applied to all of the terms in parentheses, not just the first one.
B. Second error
The second error occurred going from line 8 to line 9.
The inequality -5x ≤ -11 was incorrectly divided by -5 to get x ≤ 11/5. Multiplication or division of an inequality by a negative number is an order-reversing operation, so requires the comparison symbol be reversed.
C. How to learn it
Distributive property
The student could be asked to group some dissimilar objects, then tell what must happen to make two such groups, or three such groups. This can be compared to groups identified by parentheses, with 2 or 3 as a multiplier.
Ordering
The student can be asked to order a pair of numbers, then the same numbers with opposite signs. The direction of the comparison symbol should be noted in each case. (-1 > -2; 1 < 2) Multiplication or division by a negative can be seen as changing the signs of the things being compared.
