Chapter 8.6, Problem 1AGP

To determine

To solve : the equation

Answer to Problem 1AGP

The equation has one solution is 2

Explanation of Solution

Given information :

The equation is $\frac{2}{x+3}+\frac{3}{2}=\frac{19}{10}$

Calculation :

The LCD for the term is $10\left(x+3\right)$

  $\begin{array}{l}\frac{2}{x+3}+\frac{3}{2}=\frac{19}{10}\\ 10\left(x+3\right)\left(x+2\right)+10\left(x+3\right)=10\left(x+3\right)\frac{19}{10}\\ 10\cdot 2+5\left(x+3\right)\cdot 3=\left(x+3\right)\cdot 19\\ 20+15\left(x+3\right)=19\left(x+3\right)\\ 20+15x+45=19x+57\\ 15x+65-19x-57=0\\ -4x+8=0\\ -4x=-8\\ x=\frac{8}{4}\\ x=2\end{array}$

Check

  $\begin{array}{l}\frac{2}{x+3}+\frac{3}{2}=\frac{19}{10}\\ \frac{2}{2+3}+\frac{3}{2}=\frac{19}{10}\\ \frac{2}{5}+\frac{3}{2}=\frac{19}{10}\\ \frac{2\cdot 2+3\cdot 5}{10}=\frac{19}{10}\\ \frac{4+15}{10}=\frac{19}{10}\\ \frac{19}{10}=\frac{19}{10}\end{array}$

Hence, the equation has one solution is 2.