Question

Determine whether or not the equation below has one solution, no solutions or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.x=x+4

Answer 1

Substract x from both sides of the equation:

$x-x=x+4-x$

Add alike terms on both sides of the equation:

$0=4$

This expression is false no matter which value of x we choose.

Therefore, the equation has no solutions.

For instance, take the value x=1 and substitute into the equation:

$\begin{gathered} 1=1+4 \\ \Rightarrow \\ 1=5 \end{gathered}$

Which is false.

Another example is to take x=0.

$\begin{gathered} 0=0+4 \\ \Rightarrow \\ 0=4 \end{gathered}$

Which is false again.