###### 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 $$\{t\mid t\text{ is a real number}\}\text{.}$$

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