Chapter 8.5, Problem 20IP

To determine

The solution of the equation $\frac{2}{5}c+\frac{4}{5}c-6=c+7$ ,

Answer to Problem 20IP

  $c=65$

Explanation of Solution

Given:

The equation, $\frac{2}{5}c+\frac{4}{5}c-6=c+7$

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 $\frac{2}{5}c+\frac{4}{5}c-6=c+7$ for the variable, isolate the variable term c on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate c on left side, first simplify the like terms and then subtract both sides by $c$ and then add both sides by $6$ and then multiply both sides by $5$ and then simplify further as shown below,

  $\begin{array}{c}\frac{2}{5}c+\frac{4}{5}c-6=c+7\\ \frac{6}{5}c-6=c+7\\ \frac{6}{5}c-6-c=c+7-c\\ \frac{6c-5c}{5}-6=7\\ \frac{c}{5}-6+6=7+6\\ \frac{c}{5}=13\\ \frac{c}{5}\times 5=13\times 5\\ c=65\end{array}$

Thus, the solution of the given equation is $c=65$ .