Question

debbie solved the linear equation 3(x + 4) - 2 = 16 as follows: line 1 3(x + 4) - 2 = 16 line 2 3(x + 4) = 18 line 3 3x + 4 = 18 line 4 3x = 14 line 5 x = 4\frac{2}{3} she made an error between lines 1) 1 and 2 2) 2 and 3 3) 3 and 4 4) 4 and 5
5 subtract 3(x^2 - 2xy) from 6(x^2 - xy) and express your answer as a monomial. note: “subtract 5 from 11” means 11 - 5 = 6 pay attention to the order of your expression!

Explanation:

Step1: Analyze Debbie's work for error

In line 2, we have $3(x + 4)=18$. To get from line 2 to line 3, we should use the distributive property $a(b + c)=ab+ac$. So $3(x + 4)$ should expand to $3x+12$, not $3x + 4$. The error is between lines 2 and 3.

Step2: Solve the subtraction problem

First, expand the expressions: $6(x^{2}-xy)=6x^{2}-6xy$ and $3(x^{2}-2xy)=3x^{2}-6xy$.
Then subtract: $(6x^{2}-6xy)-(3x^{2}-6xy)=6x^{2}-6xy - 3x^{2}+6xy$.
Combine like - terms: $(6x^{2}-3x^{2})+(-6xy + 6xy)=3x^{2}$.

Answer:

1. 2) 2 and 3
2. $3x^{2}$