Chapter 4.5, Problem 8MRE

To determine

To simplify the expression

  $\left(2x+y-3\right)-\left(y+x-7\right)$

Answer to Problem 8MRE

  $x+4$

Explanation of Solution

Given:

  $\left(2x+y-3\right)-\left(y+x-7\right)$

Concept Used:

To simplify an expression first use distributive property to remove any grouping symbol, and then add/subtract like terms.

Calculation:

To simplify the expression

  $\left(2x+y-3\right)-\left(y+x-7\right)$

First remove the grouping symbols by removing parenthesis, as

  $\left(2x+y-3\right)-\left(y+x-7\right)=2x+y-3-y-x+7$

Now, add/subtract like terms in above expression:

  $\begin{array}{c}2x+y-3-y-x+7=\left(2-1\right)x+\left(1-1\right)y-3+7\\ =1x+0y+4\\ =x+4\end{array}$

Thus, simplified form of given expression is

  $\left(2x+y-3\right)-\left(y+x-7\right)=x+4$