Chapter 7.3, Problem 41CCR

To determine

Simplify the expression.

Answer to Problem 41CCR

  $2x+5(3-x)=-3x+15$

Explanation of Solution

Given:

The expression: $2x+5(3-x)$

Concept Used:

To add two or more monomials that are like terms, add the coefficients; keep the variables and exponents on the variables the same.

To subtract two or more monomials that are like terms, subtract the coefficients; keep the variables and exponents on the variables the same. on the variables the same.

Distributive Property: $a(b+c)=a·b+a·c$

Addition of Algebraic expression

In addition of algebraic expressions while adding algebraic expressions we collect the like terms and add them. The sum of several like terms is the like term whose coefficient is the sum of the coefficients of these like terms.

Example:

1. Add: 6a + 8b, 2b - 4a

Solution: 

(6a + 8b) + (2b - 4a) = 6a + 8b + 2b - 4a

Arrange the like terms together, then add. 

Thus, the required addition

= 6a - 4a + 8b + 2b = 2a + 10b

Calculation:

To add two or more monomials that are like terms, add the coefficients; keep the variables and exponents on the variables the same.

Distributive Property: $a(b+c)=a·b+a·c$

The expression: $2x+5(3-x)$

First distribute the parenthesis and then add the like terms .

  $\begin{array}{l}2x+5(3-x)\\ 2x+5·3-5·x[\text{use}\text{the}\text{rule}:a(b+c)=a·b+a·c]\\ 2x+15-5x\\ 2x-5x+15\\ -3x+15\end{array}$

  $2x+5(3-x)=-3x+15$

Thus, $2x+5(3-x)=-3x+15$