To solve the inequality \(-4t + 5 \leq -23\), follow these steps:
- Subtract 5 from both sides:
\[ -4t + 5 - 5 \leq -23 - 5 \]
This simplifies to:
\[ -4t \leq -28 \]
- Divide both sides by -4. Remember that when you divide by a negative number, you must reverse the inequality sign:
\[ t \geq 7 \]
To express the inequality with \(t\) first, we write:
\[ t >= 7 \]
So the final answer is:
\[ t >= 7 \]