Q. 2 - Elementary Algebra

Question

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

$\text{Is x}=\frac{9}{4}\text{ a solution of 4x}+9=8x?$

Step-by-Step Solution

Answer

 The given equation have the solution at $x=\frac{9}{4}$

Step 1. Given information

 Given equation is $4x+9=8x$

We have to determine whether the given value is a solution to the equation.  $\text{Is x}=\frac{9}{4}\text{ a solution of 4x}+9=8x?$

Step 2. Explanation

$\begin{array}{l}\text{Since a solution to an equation is a vlaue of the variable that makes true,}\\ \text{Being by substituting the value of the solution ofr the variable.}\\ \text{Substitute x=}\frac{9}{4}\text{ for x}\\ \Rightarrow \text{4x}+9=8x\\ \Rightarrow \text{4(}\frac{9}{4}\text{)}+9=8\left(\frac{9}{4}\right)\\ \Rightarrow \frac{9}{}\text{)}+9=\cancel{8}\left(\frac{9}{\cancel{4}}\right)\\ \Rightarrow 1\left(9\right)+9=2\left(9\right)\text{Multiply}\\ \Rightarrow 9+9=18\\ \Rightarrow 18=18\\ \text{Since x=}\frac{9}{4}\text{results true.}\\ \Rightarrow \text{x=}\frac{9}{4}\text{is a solution to the given equation}\end{array}$