Chapter 8.2, Problem 35IP

To determine

The solution of the equation $\frac{1}{4}n-20=-1$ , and check the solution.

Answer to Problem 35IP

  $n=76$

Explanation of Solution

Given:

The equation, $\frac{1}{4}n-20=-1$ .

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 $\frac{1}{4}n-20=-1$ for the unknown variable, isolate the variable term n on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate n on left side, first add 20 both sides and then multiply both sides by 4 and then simplify further as shown below,

  $\begin{array}{l}\frac{1}{4}n-20=-1\\ \frac{1}{4}n-20+20=-1+20\\ \frac{1}{4}n=19\\ \frac{1}{4}n\times 4=19\times 4\\ n=76\end{array}$

Thus, the solution of the given equation is $n=76$ .

Now, to check the solution, substitute $n=76$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}\frac{1}{4}n-20=-1\\ \frac{1}{4}\left(76\right)-20=-1\\ 19-20=-1\\ -1=-1\text{True Statement}\end{array}$

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