1. Stating the problem: Solve the equation $$|X + 1| = 5$$. 2. Recall that absolute value equation $$|A| = B$$ (where $$B \geq 0$$) can be rewritten as two separate equations: $$A = B$$ or $$A = -B$$. 3. Applying this to $$|X + 1| = 5$$: i) $$X + 1 = 5$$ ii) $$X + 1 = -5$$ 4. Solve each equation separately: For i) $$X + 1 = 5$$: Subtract 1 from both sides: $$X = 5 - 1$$ $$X = 4$$ For ii) $$X + 1 = -5$$: Subtract 1 from both sides: $$X = -5 - 1$$ $$X = -6$$ 5. Final answer: $$X = 4$$ or $$X = -6$$.