Question

Select Yes or No to indicate whether each value of x is a solution to the given equation,31x+1Yes Nox = -2x = 1DOx = 2

Answer 1

$\frac{3}{x-1}=x+1$

To find if a value of x is a solution of an equation you susbtitute the x in the equation for that value and evaluate

x=-2:

$\begin{gathered} \frac{3}{-2-1}=-2+1 \\ \\ \frac{3}{-3}=-1 \\ \\ -1=-1 \end{gathered}$

As -1 is equal to -1. x=-2 is a solution for the equation.

x=1/2

$\begin{gathered} \frac{3}{\frac{1}{2}-1}=\frac{1}{2}+1 \\ \\ \frac{3}{-\frac{1}{2}}=\frac{3}{2} \\ \\ -6=\frac{3}{2} \end{gathered}$

As -6 is not equal to 3/2, x=1/2 is not a solution for the equation

x=2

$\begin{gathered} \frac{3}{2-1}=2+1 \\ \\ \frac{3}{1}=3 \\ \\ 3=3 \end{gathered}$

As 3 is equal to 3, x=2 is a solution for the equation

x= -2, yes

x= 1/2, no

x=2, yes