Chapter 8.5, Problem 6GP

To determine

The solution of the equation $\frac{3}{8}p-3=\frac{1}{8}p-5$ ,

Answer to Problem 6GP

  $p=-8$

Explanation of Solution

Given:

The equation, $\frac{3}{8}p-3=\frac{1}{8}p-5$

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 $\frac{3}{8}p-3=\frac{1}{8}p-5$ 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 $\frac{1}{8}p$ and then add both sides by $3$ and then multiply both sides by $8$ and then multiply both sides by $2$ and then simplify further as shown below,

  $\begin{array}{c}\frac{3}{8}p-3=\frac{1}{8}p-5\\ \frac{3}{8}p-3-\frac{1}{8}p=\frac{1}{8}p-5-\frac{1}{8}p\\ \frac{2}{8}p-3=-5\\ \frac{2}{8}p-3+3=-5+3\\ \frac{2}{8}p=-2\\ \frac{2}{8}p\times 8=-2\times 8\\ 2p=-16\\ \frac{2p}{2}=\frac{-16}{2}\\ p=-8\end{array}$

Thus, the solution of the given equation is $p=-8$ .