Chapter 8.2, Problem 12GP

To determine

The solution of the equation $9=4+\frac{1}{5}q$ , and check the solution.

Answer to Problem 12GP

  $q=25$

Explanation of Solution

Given:

The equation, $9=4+\frac{1}{5}q$ .

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 $9=4+\frac{1}{5}q$ for the unknown variable, isolate the variable term q on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate q on right side, first subtract 4 from both sides and then multiply both sides by 5 and then simplify further as shown below,

  $\begin{array}{l}9=4+\frac{1}{5}q\\ 9-4=4-4+\frac{1}{5}q\\ 5=\frac{1}{5}q\\ 5\times 5=\frac{1}{5}q\times 5\\ 25=q\end{array}$

Thus, the solution of the given equation is $q=25$ .

Now, to check the solution, substitute $q=25$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}9=4+\frac{1}{5}q\\ 9=4+\frac{1}{5}\left(25\right)\\ 9=4+5\\ 9=9\text{True Statement}\end{array}$

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