Chapter 8, Problem 20CR

To determine

The solution of the equation $\frac{4}{5}\left(c+12\right)=-8$ ,

Answer to Problem 20CR

  $c=2$

Explanation of Solution

Given:

The equation, $\frac{4}{5}\left(c+12\right)=-8$

Concept Used:

Left distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

• 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 $\frac{4}{5}\left(c+12\right)=-8$ 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 use Left distributive property and then subtract both sides by $\frac{48}{5}$ and then multiply both sides by $5$ and then divide both sides by $4$ and then simplify further as shown below,

  $\begin{array}{c}\frac{4}{5}\left(c+12\right)=-8\\ \frac{4}{5}\cdot c-\frac{4}{5}\cdot 12=-8\\ \frac{4c}{5}-\frac{48}{5}=-8\\ \frac{4c}{5}-\frac{48}{5}+\frac{48}{5}=-8+\frac{48}{5}\\ \frac{4c}{5}=-8\times \frac{5}{5}+\frac{48}{5}\\ \frac{4c}{5}=\frac{-40}{5}+\frac{48}{5}\\ \frac{4c}{5}=\frac{8}{5}\\ \frac{4c}{5}\times 5=\frac{8}{5}\times 5\\ 4c=8\\ \frac{4c}{4}=\frac{8}{4}\\ c=2\end{array}$

Thus, the solution of the given equation is $c=2$ .