Chapter 2.1, Problem 24P

Solve each equation. Check your answer.

$a+1\frac{1}{4}=2\frac{7}{10}$

To determine

To solve the equation:

  $a+1\frac{1}{4}=2\frac{7}{10}$

And also check the solution.

Answer to Problem 24P

  $a=\frac{29}{20}$

Explanation of Solution

Given:

  $a+1\frac{1}{4}=2\frac{7}{10}$

Concept Used:

• Steps to solve a linear equation:
1. Use distributive property to remove any grouping symbol.
2. Simplify the expression in each side of the equation.
3. Collect the variable terms on one side of the equation and the constant on the other side.
4. Isolate the variable
• To check the solution of a equation substitute the solution in the equation and check whether it satisfies.

Calculation:

In order to solve the equation:

  $a+1\frac{1}{4}=2\frac{7}{10}$

First, simplify the both sides by converting mixed fractions into simple fractions as,

  $\begin{array}{l}a+1\frac{1}{4}=2\frac{7}{10}\\ a+\frac{4\left(1\right)+1}{4}=\frac{10\left(2\right)+7}{10}\\ a+\frac{5}{4}=\frac{27}{10}\end{array}$

Now isolate the variables of equation by subtracting $\frac{5}{4}$ on both sides as,

  $\begin{array}{l}a+\frac{5}{4}-\frac{5}{4}=\frac{27}{10}-\frac{5}{4}\\ \Rightarrow a=\frac{27\left(4\right)-5\left(10\right)}{10\left(4\right)}\\ \Rightarrow a=\frac{108-50}{40}\\ \Rightarrow a=\frac{58}{40}\\ \Rightarrow a=\frac{29}{20}\end{array}$

Thus, solution of given equation is $a=\frac{29}{20}$ .

Now, to check this solution put $a=\frac{29}{20}$ in left hand side of the given equation, and check whether both sides are equal. As,

  $\begin{array}{c}\frac{29}{20}+\frac{5}{4}=\frac{116+100}{80}\\ =\frac{216}{80}=\frac{54}{20}\\ =\frac{27}{10}\\ =\text{Right Hand side}\end{array}$

Thus, $a=\frac{29}{20}$ is correct solution for given equation.