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Video: Writing an Inequality to Represent a Constraint or Condition in a Real-World Problem

Bethani Gasparine

Ernest walked for 29 minutes before reaching the university campus. He took at least another 5 minutes to reach the lecture hall. Write an inequality that represents the amount of time it took Ernest to reach the lecture hall.

02:17

Video Transcript

Ernest walked for twenty-nine minutes before reaching the university campus. He took at least another five minutes to reach the lecture hall. Write an inequality that represents the amount of time it took Ernest to reach the lecture hall.

Since we’re writing an inequality to represent the amount of time it took Ernest to reach the lecture hall, we need the twenty-nine minutes to campus plus the extra five minutes that it took to get to the lecture hall. And the keyword is it took “at least” five minutes to get to the lecture hall. That will help us decide the inequality sign. At least five minutes means it took him five minutes or more to get to the lecture hall. So that can represent exactly five minutes or anything over five minutes such as six minutes or seven minutes or eight and a half minutes.

So the least or the shortest amount of time that it would take him to get to the lecture hall would be twenty-nine plus five minutes because it took him at least five minutes, so five minutes or more. So the shortest amount of time it would’ve taken him would be twenty-nine plus five. So thirty four minutes would’ve been the shortest possible time.

So it would’ve taken him thirty-four minutes or more. When you’re gonna say “or more”, you need to use the word “at least”. Thirty-four would be the least amount of time that it would take Ernest to reach the lecture hall.

So if we would let 𝑥 represent the total amount of time for him to reach the lecture hall, we would have 𝑥 is greater than or equal to thirty-four minutes because this means 𝑥 can be equal to thirty-four minutes, so it could’ve taken him thirty-four minutes, or 𝑥 is greater than thirty-four minutes. So that could be thirty-five, thirty-six, thirty-seven, and so on.

Therefore, an inequality that represents the amount of time it took Ernest to reach the lecture hall would be: 𝑥 is greater than or equal to thirty-four minutes.