Chapter 8, Problem 11CR

To determine

The solution of the equation $\frac{1}{3}a+2=5$ ,

Answer to Problem 11CR

  $a=9$

Explanation of Solution

Given:

The equation, $\frac{1}{3}a+2=5$

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 $\frac{1}{3}a+2=5$ for the variable, isolate the variable term a on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate a on left side, first subtract both sides by $2$ and then multiply both sides by $3$ and then simplify further as shown below,

  $\begin{array}{c}\frac{1}{3}a+2=5\\ \frac{1}{3}a+2-2=5-2\\ \frac{1}{3}a=3\\ \frac{1}{3}a\times 3=3\times 3\\ a=9\end{array}$

Thus, the solution of the given equation is $a=9$ .