Chapter 8.4, Problem 5GP

To determine

The solution of the equation $\frac{1}{3}\left(c-4\right)=12$ .

Answer to Problem 5GP

  $c=40$

Explanation of Solution

Given:

The equation, $\frac{1}{3}\left(c-4\right)=12$ .

Concept Used:

Distributive property:

Left Distributive property: $a\left(b\pm c\right)=a\cdot b\pm a\cdot c$

Right Distributive property: $\left(a\pm b\right)c=a\cdot c\pm b\cdot c$

• 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 $\frac{1}{3}\left(c-4\right)=12$ for the unknown variable, first using left Distributive property in left side of the equation and then 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 add 4/3 both sides and then multiply both sides by 3 and then simplify further as shown below,

  $\begin{array}{l}\frac{1}{3}\left(c-4\right)=12\\ \frac{1}{3}\cdot c-\frac{1}{3}\cdot 4=12\\ \frac{1}{3}c-\frac{4}{3}=12\\ \frac{1}{3}c-\frac{4}{3}+\frac{4}{3}=12+\frac{4}{3}\\ \frac{1}{3}c=\frac{40}{3}\\ \frac{1}{3}c\times 3=\frac{40}{3}\times 3\\ c=40\end{array}$

Thus, the solution of the given equation is $c=40$ .