The incorrect step in Mai's and Noah's solution are presented as follows;
The incorrect step in Mai's solution; 7·x + 3 = 3(9)
The incorrect step in Noah's solution; 27·x + 3 = 27
The details on why the step are incorrect can be presented as follows;
The solution to the equation 14·x - 2·x + 3 = 3·(5·x + 9) can be presented as follows;
14·x - 2·x + 3 = 3·(5·x + 9)
12·x + 3 = 15·x + 27
12·x - 15·x = 27 - 3
-3·x = 24
x = 24/(-3)
x = -8
The incorrect steps in the solution are;
The incorrect step in Mai's solution is the step; 7·x + 3 = 3(9)
The previous equation before the step 12·x + 3 = 3·(5·x + 9), can be expanded to get;
12·x + 3 = 15·x + 27
Therefore, Mai subtracted 7·x from 12·x to get 5·x rather than 15·x from 12·x to get (-3·x)
The incorrect step in Noah's solution is the step 27·x + 3 = 27
The previous equation before the step 12·x + 3 = 15·x + 27, indicates that collecting like terms, we get;
On the left hand side; 12·x - 15·x = -3·x
However Noah may have evaluated 12·x + 15·x = 27·x
Therefore, there terms 12·x and 15·x are added rather than subtracted in the step
The complete question found through search can be presented as follows;
Mai and Noah also solved the equation but some of their steps have errors. Find the incorrect step in each solution and explain why it is incorrect
Mai
14·x - 2·x + 3 = 3·(5·x + 9)
12·x + 3 = 3·(5·x + 9)
7·x + 3 = 3(9)
7·x + 3 = 27
7·x = 24
x = 24/7
Noah
14·x - 2·x + 3 = 3·(5·x + 9)
12·x + 3 = 15·x + 27
27·x + 3 = 27
27·x = 24
x = 24/27