Chapter 4, Problem 25SGR

To determine

To solve and check: the given equation

Answer to Problem 25SGR

The solution of the given equation is $x=\frac{109}{20}$ .

Explanation of Solution

Given:

  $x+3\frac{1}{4}=2\frac{1}{5}$

Calculation:

  $\begin{array}{l}x-3\frac{1}{4}=2\frac{1}{5}\\ x-\frac{13}{4}=\frac{11}{5}\text{ simplyfy }\end{array}$

Taking L.C.M.,

  $\begin{array}{l}\frac{4x-13}{4}=\frac{11}{5}\\ 5\left(4x-13\right)=11\left(4\right)\text{ cross multiplication}\\ \text{20x}-5\left(13\right)=44\text{ distributive property}\\ 20x-65=44\\ 20x=44+65\text{ making like term together}\\ 20x=109\\ x=\frac{109}{20}\end{array}$

To check the solution, putting the value of x in the given equation,

  $\begin{array}{l}L.H.S=x-3\frac{1}{4}\\ \text{ =}\frac{109}{20}-\frac{13}{4}\\ \text{ = }\frac{109-65}{20}\\ =\frac{44}{20}\\ =\frac{11}{5}\\ =2\frac{1}{5}\\ \text{ = R}\text{.H}\text{.S}\end{array}$ Putting $x=\frac{109}{20}$

Conclusion:

Hence, the solution of the given equation is $x=\frac{109}{20}$ .