Chapter 8, Problem 13CR

To determine

The solution of the equation $\frac{4}{7}+2p=\frac{2}{7}$ ,

Answer to Problem 13CR

  $p=\frac{-1}{7}$

Explanation of Solution

Given:

The equation, $\frac{4}{7}+2p=\frac{2}{7}$

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 $\frac{4}{7}+2p=\frac{2}{7}$ for the 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 subtract both sides by $\frac{4}{7}$ and then divide both sides by $2$ and then simplify further as shown below,

  $\begin{array}{c}\frac{4}{7}+2p=\frac{2}{7}\\ \frac{4}{7}+2p-\frac{4}{7}=\frac{2}{7}-\frac{4}{7}\\ 2p=\frac{-2}{7}\\ \frac{2p}{2}=\frac{-2}{7\times 2}\\ p=\frac{-1}{7}\end{array}$

Thus, the solution of the given equation is $p=\frac{-1}{7}$ .