Example 3.6.6

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 \(\{t\mid t\text{ is a real number}\}\text{.}\)