Chapter 8.2, Problem 23GP

To determine

The solution of the equation $\frac{1}{3}p+6-\frac{2}{3}p=0$ , and check the solution.

Answer to Problem 23GP

  $p=18$

Explanation of Solution

Given:

The equation, $\frac{1}{3}p+6-\frac{2}{3}p=0$ .

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 $\frac{1}{3}p+6-\frac{2}{3}p=0$ for the unknown variable, isolate the variable term p on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate p on left side, first combining both the p terms and then subtract 6 from both sides and then multiply both sides by -3 and then simplify further as shown below,

  $\begin{array}{l}\frac{1}{3}p+6-\frac{2}{3}p=0\\ -\frac{1}{3}p+6=0\\ -\frac{1}{3}p+6-6=0-6\\ -\frac{1}{3}p\times -3=-6\times -3\\ p=18\end{array}$

Thus, the solution of the given equation is $p=18$ .

Now, to check the solution, substitute $p=18$ in the given equation and check whether the values on both sides of equal sign is same or no. So, it gives

  $\begin{array}{l}\frac{1}{3}p+6-\frac{2}{3}p=0\\ \frac{1}{3}\times 18+6-\frac{2}{3}\times 18=0\\ 6+6-12=0\\ 0=0\text{True Statement}\end{array}$

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