Question

1. nora and so - hee each solve the equation 2(6 - 4x)=-2x - 2 in different ways.

noras work
2(6 - 4x)=-2x - 2
2(6)-4x=-2x - 2
12 - 4x=-2x - 2
12 - 4x + 4x=-2x + 4x - 2
12 = 2x - 2
12 + 2 = 2x - 2 + 2
14 = 2x
1/2(14)=1/2(2x)
7 = x
the solution is 7.
so - hees work
2(6 - 4x)=-2x - 2
1/2(2(6 - 4x))=1/2(-2x - 2)
6 - 4x=-x - 1
6 - 4x + x=-x + x - 1
6 - 3x=-1
6+( - 6)-3x=-1+( - 6)
-3x=-7
-1/3(-3x)=-1/3(-7)
x = 7/3
the solution is 7/3.
a. which students solution shows a correct method for solving the equation?
b. in the incorrect solution, circle the step that first shows an error.
c. explain why the step you circled is incorrect.

Explanation:

Step1: Analyze Nora's work

Nora made an error in the second - step. When using the distributive property $a(b - c)=ab - ac$, for $2(6 - 4x)$, it should be $2\times6-2\times4x = 12-8x$, not $2(6)-4x$.

Step2: Analyze So - hee's work

So - hee correctly applied the distributive property and the properties of equality (addition, subtraction, multiplication, and division) to solve the equation. She first multiplied both sides of the equation by $\frac{1}{2}$, then added $x$ to both sides, and then subtracted 6 from both sides, and finally divided both sides by - 3 to get the correct solution.

Answer:

a. So - hee's solution shows a correct method for solving the equation.
b. In Nora's solution, the step $2(6)-4x=-2x - 2$ is the first step that shows an error.
c. The error is that when applying the distributive property $a(b - c)=ab - ac$ to $2(6 - 4x)$, Nora did not multiply 4x by 2. It should be $2\times6-2\times4x=12 - 8x$, not $12-4x$.