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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

User CaffeinatedCM
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1 Answer

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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.

User Pedro Vale
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