How is an inequality different from an equation? Give a real-world scenario in which you would write an inequality rather than an equation.
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An inequality is different from an equation because it represents a relationship between two or more values that may not be equal. In contrast, an equation represents a relationship in which two values are exactly equal.
A real-world scenario where you would write an inequality rather than an equation is when buying groceries on a budget. Let's say you have a limited amount of money, let's say $50, to spend on groceries. You want to ensure that the total cost of the groceries you purchase does not exceed your budget.
In this scenario, you would write an inequality, such as:
Total cost of groceries ≤ $50
The inequality symbol (≤) indicates that the total cost of groceries should be less than or equal to $50. This allows for the possibility of spending the entire budget or less, but not exceeding it.
Let's suppose you want to buy apples (A) and bananas (B), and their prices are $2 per apple and $1 per banana. You can represent this situation as an inequality:
2A + 1B ≤ 50
This inequality states that the total cost of apples and bananas should be less than or equal to $50. You can adjust the quantities of apples and bananas as long as the total cost remains within your budget.
By solving the inequality, you can determine the permissible combinations of apples and bananas that satisfy your budget constraint.