1. **State the problem:** Solve the inequality $$22 \leq x + 3$$ for $$x$$. 2. **Formula and rules:** To isolate $$x$$, subtract 3 from both sides of the inequality. When subtracting or adding the same number on both sides, the inequality direction remains the same. 3. **Intermediate work:** $$22 \leq x + 3$$ Subtract 3 from both sides: $$22 - 3 \leq x + 3 - 3$$ Show cancellation: $$22 - \cancel{3} \leq x + \cancel{3}$$ Simplify: $$19 \leq x$$ 4. **Final answer:** $$x \geq 19$$ This means $$x$$ must be greater than or equal to 19 to satisfy the inequality.