Q. 4 - Elementary Algebra

Question

In the following exercise, determine whether the given value is a solution to the equation. 

$\text{Is v}=-\frac{1}{3}\text{ a solution of 9v-2}=3v?$

Step-by-Step Solution

Answer

No

Step 1. Given informaiton

In the following exercise, determine whether the given value is a solution to the equation. 

$\text{Is v}=-\frac{1}{3}\text{ a solution of 9v-2}=3v?$

Step 2. Explanation

$\begin{array}{l}\text{Since a solution to an equation is a vlaue of the variable that makes true,}\\ \text{Being by substituting the value of the solution ofr the variable.}\\ \text{Substitute v}=-\frac{1}{3}\text{ for v}\\ \Rightarrow \text{9v-2}=3v\\ \Rightarrow 9\text{(-}\frac{1}{3}\text{)-2}=3\text{(-}\frac{1}{3}\text{)}\\ \Rightarrow \cancel{9}\text{(-}\frac{1}{\cancel{3}}\text{)-2}=\cancel{3}\text{(-}\frac{1}{\cancel{3}}\text{)}\\ \Rightarrow 3(-1)-2=1(-1)\text{Multiply}\\ \Rightarrow -3-2=1(-1)\\ \Rightarrow -5=-1\\ \text{Since v}=-\frac{1}{3}\text{results false.}\\ \Rightarrow \text{v}=-\frac{1}{3}\text{is not a solution to the given equation}\end{array}$