Jenny simplified the expression 7x + 5y + 4(x – y) – 6 and listed the Number Properties used:
c) Redo the problem correctly.
Justify each step using the
correct Number Property. (2 points)
Jenny’s Work Number Property Used
7x + 5y + 4(x – y) – 6 Given
1) 7x + 5y + 4x – y – 6 Distributive Property
2) (7x + 4x) + (5y – y) – 6 Associative Property of Addition
3) 11x + 4y – 6 Combine Like Terms
a) Circle the mistake(s) that Jenny made. Describe what
she did incorrectly. What should she have done?
There may be more than one mistake! (2 points)
b) Name one thing she did correctly. (1 point)
a) Jenny made two mistakes in her simplification. First, in step 2, she incorrectly applied the Associative Property of Addition. Instead of grouping the terms (7x + 4x) and (5y - y), she should have grouped the terms (7x + 4(x – y)) and (5y – 6). Second, in step 3, she incorrectly combined the terms 4x and 4(x – y) as 11x. She should have kept them separate.
To correct her mistakes, Jenny should have applied the Distributive Property correctly in step 2. She should have multiplied 4 with both x and (x - y), resulting in 4x - 4y. Then, instead of combining the terms (7x + 4x) and (5y - y), she should have combined (7x + 4x) and (4x - 4y) to get 11x + 4x - 4y. Finally, she should have combined the like terms to simplify the expression to 15x - 4y - 6.
b) One thing that Jenny did correctly is that she correctly applied the Distributive Property in step 1 by multiplying 4 with (x - y) to get 4x - 4y.