Question

1. $t + 14 \geq 15$ or $t - 9 < -10$
2. $-3 \leq 7c + 4 < 18$
3. $22 \geq 4m - 2$ or $5 - 3m \leq -13$

Explanation:

Step1: Solve \(22 \geq 4m - 2\)

Add 2 to both sides: \(22 + 2 \geq 4m - 2 + 2\)
\(24 \geq 4m\)
Divide by 4: \(\frac{24}{4} \geq \frac{4m}{4}\)
\(6 \geq m\) or \(m \leq 6\)

Step2: Solve \(5 - 3m \leq -13\)

Subtract 5: \(5 - 3m - 5 \leq -13 - 5\)
\(-3m \leq -18\)
Divide by -3 (reverse inequality): \(\frac{-3m}{-3} \geq \frac{-18}{-3}\)
\(m \geq 6\)

Step3: Combine solutions

The "or" means union of \(m \leq 6\) and \(m \geq 6\), so \(m\) is all real numbers (since \(m \leq 6\) or \(m \geq 6\) covers every real \(m\)).

Answer:

All real numbers (or \(m \in \mathbb{R}\))