What inequality represents the sentence the product of a number and 12 is no more than 15 answers are 12n<15, 12n>15, 12n>15line under the>, 12n<15line under the<
12n ≤ 15
The inequality that represents the sentence "the product of a number and 12 is no more than 15" is 12n ≤ 15.
To understand why this is the correct inequality, let's break down the sentence. The phrase "the product of a number and 12" means we multiply a number, which we represent with n, by 12. So, the product can be represented as 12n.
The phrase "is no more than" indicates that we need an inequality that represents a value being less than or equal to the other value. In this case, the value is 15, so we have 12n ≤ 15.
Let's look at the other answer options to explain why they are not correct:
- 12n < 15: This inequality represents the product of a number and 12 being strictly less than 15, but does not include the possibility of being equal to 15. However, our sentence specifically states "no more than 15," which includes the possibility of equality.
- 12n > 15: This inequality represents the product of a number and 12 being strictly greater than 15, which is the opposite of what our sentence states. The sentence states "no more than 15," indicating values that are less than or equal to 15.
- 12n > 15 with a line under the '>' symbol: In mathematics, a line placed under a symbol such as '>' typically represents "greater than or equal to." However, our sentence specifically states "no more than 15," which means less than or equal to 15. Therefore, the line under the '>' symbol is not appropriate in this case.
Therefore, the correct inequality to represent the sentence "the product of a number and 12 is no more than 15" is: 12n ≤ 15.