Question Video: Optimization Using Inequalities | Nagwa Question Video: Optimization Using Inequalities | Nagwa

Question Video: Optimization Using Inequalities Mathematics

Given that −3 ≤ 𝑥 ≤ 10 and −2 ≤ 𝑦 ≤ 10, find the greatest possible value of 𝑦 − 𝑥.

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Video Transcript

Given that 𝑥 is greater than or equal to negative three and less than or equal to 10 and 𝑦 is greater than or equal to negative two and less than or equal to 10, find the greatest possible value of 𝑦 minus 𝑥.

In this question, we are trying to calculate the greatest value of the expression 𝑦 minus 𝑥. As we are trying to find the difference between the two values, we need the first variable 𝑦 to be as large as possible. We are therefore looking for the maximum value of 𝑦. The maximum value of 𝑦 is 10, as 𝑦 must be less than or equal to 10.

We need the second variable 𝑥 to be as small as possible. We are therefore looking for the minimum value of 𝑥. This is equal to negative three, as 𝑥 must be greater than or equal to negative three. This means that in order to find the greatest possible value of 𝑦 minus 𝑥, we need to subtract negative three from 10. This is the same as adding three to 10. 10 plus three is equal to 13. If 𝑥 is greater than or equal to negative three and less than or equal to 10 and 𝑦 is greater than or equal to negative two and less than or equal to 10, then the greatest possible value of 𝑦 minus 𝑥 is 13.

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