How is an inequality different from an equation? Give a real-world scenario in which you would write an inequality rather than an equation.
I don't know how to solve this or what the answer is. Please help!
An equation show two equal entities. An inequality shows that one is larger than the other.
An example of an inequality:
Denise has $50 and wants to buy two new shirts. She needs to know how the average price she'll need to pay so that she doesn't exceed her $50.
2n < 50
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An inequality is different from an equation because it represents a relationship between two values that may not be equal. In an inequality, there is a comparison between two quantities using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to). On the other hand, an equation indicates that the two sides of the equation are equal.
To understand the difference, let's consider a real-world scenario:
Scenario:
Suppose you're in a store and you want to buy a shirt. Let's say the regular price of the shirt is $30. Now, let's explore two different situations involving equations and inequalities:
1. Equation:
If you have a $30 coupon for the store, and you want to know how much money you have to pay, you can use an equation. Let's call the amount of money you have to pay "x". Using an equation, you would write:
$30 - $30 coupon = x
By solving this equation, you would find that x equals $0. This implies that after using the coupon, you would not have to pay anything for the shirt.
2. Inequality:
However, let's consider a different scenario. If you only have a $20 coupon, you would need to write an inequality to represent how much money you would have to pay. Let's again call the amount of money you have to pay "x". Using an inequality, you would write:
$30 - $20 coupon > x
This inequality states that the difference between the regular price of the shirt ($30) and the value of the coupon ($20) must be greater than the amount you have to pay ($x). By simplifying the inequality, you find that $10 must be greater than x. This implies that you would have to pay more than $10 for the shirt, even after using the coupon.
To summarize, an inequality allows for comparisons between two values and considers the possibility of one value being greater or less than the other. In contrast, an equation represents a balance or equivalence between two values.