###### Example3.5.6

Solve for \(t\) in the inequality \(4t+5\gt 4t+2\text{.}\)

To solve for \(t\text{,}\) we will first subtract \(4t\) from each side to get all terms containing \(t\) on one side:

\begin{align*}
4t+5\amp\gt 4t+2\\
4t+5\subtractright{4t}\amp\gt 4t+2\subtractright{4t}\\
5\amp\gt 2
\end{align*}

Notice that again, the variable \(t\) is no longer contained in the inequality. We then need to consider which values of \(t\) make the inequality true. The answer is *all values*, so our solution set is all real numbers, which we can write as \(\{t\mid t\text{ is a real number}\}\text{.}\)