Chapter 8.2, Problem 38IP

To determine

The solution of the equation $\frac{1}{4}t+1=2\frac{1}{4}$ , and check the solution.

Answer to Problem 38IP

  $t=5$

Explanation of Solution

Given:

The equation, $\frac{1}{4}t+1=2\frac{1}{4}$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation $\frac{1}{4}t+1=2\frac{1}{4}$ for the unknown variable, isolate the variable term t on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate t on left side, first subtract 1 from both sides and then multiply both sides by 4 and then simplify further as shown below,

  $\begin{array}{l}\frac{1}{4}t+1=2\frac{1}{4}\\ \frac{1}{4}t+1=\frac{9}{4}\\ \frac{1}{4}t+1-1=\frac{9}{4}-1\\ \frac{1}{4}t=\frac{5}{4}\\ \frac{1}{4}t\times 4=\frac{5}{4}\times 4\\ t=5\end{array}$

Thus, the solution of the given equation is $t=5$ .

Now, to check the solution, substitute $t=5$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}\frac{1}{4}t+1=2\frac{1}{4}\\ \frac{1}{4}\left(5\right)+1=\frac{9}{4}\\ \frac{5}{4}+1=\frac{9}{4}\\ \frac{5+4}{4}=\frac{9}{4}\\ \frac{9}{4}=\frac{9}{4}\text{True statementy}\end{array}$

Since, the left hand side and right hand side are equal, so the solution is correct.