1. The problem asks to classify the equation $$24x + 1 = 24x + 68$$ as having one solution, no solution, or infinitely many solutions. 2. Start by subtracting $$24x$$ from both sides: $$24x + 1 = 24x + 68$$ $$\cancel{24x} + 1 = \cancel{24x} + 68$$ which simplifies to: $$1 = 68$$ 3. Since $$1 \neq 68$$, this is a contradiction, meaning the equation has no solution. 4. Next, write examples of each type: - One solution: $$8x + 24 = 7x + 24$$ - No solution: $$8x + 24 = 8x + 23$$ - Infinitely many solutions: $$8x + 24 = 8x + 24$$ 5. Now, classify the given multiple choice equations: - One solution: Equation A ($$8x + 24 = 7x + 24$$) because subtracting $$7x$$ leaves $$x = 0$$. - No solution: Equation B ($$8x + 24 = 8x + 23$$) because subtracting $$8x$$ leaves $$24 = 23$$, a contradiction. - Infinitely many solutions: Equation B ($$8x + 24 = 8x + 24$$) because both sides are identical. Final answers: - The original equation has no solution. - One solution equation: $$8x + 24 = 7x + 24$$ - No solution equation: $$8x + 24 = 8x + 23$$ - Infinitely many solutions equation: $$8x + 24 = 8x + 24$$