Chapter 1.3, Problem 55PPSE

Solution

To state: If the simplified expression is correct.

The correct answer of the expression $-\left(x+y\right)+3\left(x-4y\right)$ is $2x-13y$ .

Given information:

The given expression is $-\left(x+y\right)+3\left(x-4y\right)$ .

Explanation:

Consider the given simplification:

  $\begin{array}{c}-\left(x+y\right)+3\left(x-4y\right)=-x+y+3x-4y\\ =2x-3y\end{array}$

The given simplification is wrong. It can be seen that while simplifying this expression John removed the brackets (grouping symbols) directly. He did not multiplied 3 to $\left(x-4y\right)$ but he only multiplied 3 to x .

Correct simplification of the expression $-\left(x+y\right)+3\left(x-4y\right)$ :

  $-\left(x+y\right)+3\left(x-4y\right)$ .

Remove grouping symbol and identify the like terms,

  $-x-y+3x-12y$ .

Use Commutative property,

  $\left(-1+3\right)x+\left(-1-12\right)y$ .

Combine like terms and simplify,

  $2x-13y$ .

Therefore, the correct answer is $2x-13y$ .