Chapter 8, Problem 23CR

To determine

The solution of the equation $\frac{3}{8}\left(v-6\right)=\frac{1}{8}$ ,

Answer to Problem 23CR

  $v=6.33$

Explanation of Solution

Given:

The equation, $\frac{3}{8}\left(v-6\right)=\frac{1}{8}$

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 $\frac{3}{8}\left(v-6\right)=\frac{1}{8}$ for the variable, isolate the variable term v on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate v on left side, first use Left distributive property and then add both sides by $\frac{18}{8}$ and then multiply both sides by $8$ and then divide both sides by $3$ and then simplify further as shown below,

  $\begin{array}{c}\frac{3}{8}\left(v-6\right)=\frac{1}{8}\\ \frac{3}{8}\cdot v+\frac{3}{8}\cdot \left(-6\right)=\frac{1}{8}\\ \frac{3v}{8}-\frac{18}{8}=\frac{1}{8}\\ \frac{3v}{8}-\frac{18}{8}+\frac{18}{8}=\frac{1}{8}+\frac{18}{8}\\ \frac{3v}{8}=\frac{19}{8}\\ \frac{3v}{8}\times 8=\frac{19}{8}\times 8\\ 3v=19\\ \frac{3v}{3}=\frac{19}{3}\\ v=6.33\end{array}$

Thus, the solution of the given equation is $v=6.33$ .