Q. 2.1 - Elementary Algebra

Question

$Is y = \frac{4}{3} a solution of 9y + 2 = 6y + 3 ?$

Step-by-Step Solution

Answer

The given value $y=\frac{4}{3}$is not the solution for the given equation.

Step 1. Given information

The given equation is $9y + 2 = 6y + 3$

We have to determine the given value $y=\frac{4}{3}$ is the solution of the given equation.

Step 2. Explanation

$\begin{array}{l}Sinceasolutiontoanequationisavalueof\text{ the variable that makes the equation true,}\\ \text{Begin by substituting the value of the solution for the variable. }\\ \text{Substitute y=}\frac{4}{3}\text{ for y}\\ \Rightarrow 9y + 2 = 6y + 3 \\ \Rightarrow \cancel{9}\left(\frac{4}{\cancel{3}}\right) + 2 = \cancel{6}\left(\frac{4}{\cancel{3}}\right) + 3\\ \text{Multiply}\\ \Rightarrow 3\left(4\right)+2=2\left(4\right)+3\\ \Rightarrow 12+2=8+3\\ \text{Add}\\ \Rightarrow 14=11\\ \text{Since y=}\frac{4}{3}\text{ results in a false equation.}\\ \Rightarrow \frac{4}{3}\text{is not a solution to the given equation.}\end{array}$