Chapter 7.3, Problem 16IP

To determine

Add the expression.

Answer to Problem 16IP

  $\frac{11}{2}x+\frac{5}{3}$

Explanation of Solution

Given:

The expression: $(3\frac{1}{2}x-\frac{2}{3})+(-\frac{1}{4}x+1\frac{1}{2})+(-1\frac{3}{4}x+\frac{5}{6})+(4x)$

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.

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.

The expression: $(3\frac{1}{2}x-\frac{2}{3})+(-\frac{1}{4}x+1\frac{1}{2})+(-1\frac{3}{4}x+\frac{5}{6})+(4x)$

Add the like terms and the numbers separately.

  $\begin{array}{l}(3\frac{1}{2}x-\frac{2}{3})+(-\frac{1}{4}x+1\frac{1}{2})+(-1\frac{3}{4}x+\frac{5}{6})+(4x)\\ (3\frac{1}{2}x+-\frac{1}{4}x+-1\frac{3}{4}x+4x)+(-\frac{2}{3}+1\frac{1}{2}+\frac{5}{6})\\ (\frac{7}{2}x-\frac{1}{4}x-\frac{7}{4}x+\frac{4}{1}x)+(-\frac{2}{3}+\frac{3}{2}+\frac{5}{6})\\ (\frac{14}{4}x-\frac{1}{4}x-\frac{7}{4}x+\frac{16}{4}x)+(-\frac{4}{6}+\frac{9}{6}+\frac{5}{6})\\ (\frac{14-1-7+16}{4}x)+(\frac{-4+9+5}{6})\\ (\frac{22}{4}x)+(\frac{10}{6})\\ \frac{11}{2}x+\frac{5}{3}\end{array}$ $(3\frac{1}{2}x-\frac{2}{3})+(-\frac{1}{4}x+1\frac{1}{2})+(-1\frac{3}{4}x+\frac{5}{6})+(4x)=\frac{11}{2}x+\frac{5}{3}$

Thus, $(3\frac{1}{2}x-\frac{2}{3})+(-\frac{1}{4}x+1\frac{1}{2})+(-1\frac{3}{4}x+\frac{5}{6})+(4x)=\frac{11}{2}x+\frac{5}{3}$