Subjects algebra

Money Inequality

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1. The problem states: You have 37 units of money and need to save 3 units for bus fare. We want to find the inequality representing the amount of money $m$ you can spend. 2. Since you must save 3 units, the money spent plus the saved money should be less than or equal to 37: $$m + 3 \leq 37$$ 3. Rearranging the inequality to isolate $m$: $$m \leq 37 - 3$$ 4. Simplifying the right side: $$m \leq 34$$ 5. This means you can spend at most 34 units of money. 6. Now, let's check the given inequalities: - $37 - m > 3$ can be rewritten as $m < 34$, which is similar but strict inequality. - $3 < m + 37$ simplifies to $m > -34$, which is not relevant here. - $37 - m \geq 3$ simplifies to $m \leq 34$, which matches our derived inequality. - $m \leq 37 + 3$ simplifies to $m \leq 40$, which is incorrect since you only have 37. 7. Therefore, the correct inequality representing the amount of money you can spend is: $$37 - m \geq 3$$ or equivalently $$m \leq 34$$ Final answer: $37 - m \geq 3$