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### Section 2.1 : Solutions and Solution Sets

3. Is $$t = - 3$$ a solution to $${t^2} + 3t - 10 = 4 + 8t$$?

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There really isn’t all that much to do for these kinds of problems. All we need to do is plug the given number into both sides of the equation and check to see if the right and left side are the same value.

Here is that work for this particular problem.

\begin{align*}{\left( { - 3} \right)^2} + 3\left( { - 3} \right) - 10 & \mathop = \limits^? 4 + 8\left( { - 3} \right)\\ - 10 & = - 20\,\,\,\,{\mbox{NOT OK}}\end{align*}

So, we can see that the right and left sides are the not the same and so we know that $$t = - 3$$ is not a solution to the equation.