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# Solving two-variable inequalities word problem

Given a two-variable linear inequality that models a context about watering plants, Sal finds how many flowers can be watered.

## Want to join the conversation?

• At Sal said that "We don't have to change the inequality because we are dividing by a positive number." Is there a video on when you do have to flip the inequality around? I have not found one.
• Couldn't the answer be he can water 8 plants and then he has a little bit of extra water left to partially water a 9th plant?
• Yes, in the real world that's exactly what we'd do, but the question was asking for how many plants can be watered. That is, how many whole plants can be watered. If the question was adjusted we could give the answer as 8 4/7.
• at around Sal converts 0.7 into 7/10 then while dividing 6/0.7 flips 7/10 to 10/7 & multiplies is there a name for this process?
• How to write an inequality when its says "At most" and when it says "At least"?
(1 vote)
• At most is a maximum word which is ≤ and at least is a minimum word which is ≥. Think of grades in school, what do you need to pass (at least a 70) which means you could get higher, but no lower. What is the most you can get for a class (at most 100), you can get lower, but no higher.
• i'm still confused is there a way this can be explained better to me
• Why are you using fractions and not decimals? I was surprised to see that. I did 6/0.7 = 8.6 as the answer.
(1 vote)
• Fractions are much easier to work with and are easily reducible. So most of the people prefer to work with fractions. For example, 6/0.7 is 8.57142857 in decimal so , 8.6 is not a very accurate value but it is okay if the questions asks you to round up to nearest tenth. But if you want to use the value for further calculations , stick with fractions for the sake of accuracy.
• Help with this? The answer is 3 m/s, but I cannot figure out how to arrive there.

" Guliskhan plans to cover a certain distance by running and bicycling. She runs at a constant speed, and she bicycles at a speed of 7 meters per second

Let R represent the number of seconds that Guliskhan runs and B represent the number of seconds that she bicycles according to her plan.

3R+7B≥1000,

According to the inequality, at what speed does Guliskhan run, and what is the minimum distance that she plans to cover? "
• It looks like the questions are designed to see if you understand what the numbers and variables in the inequality represent.
Look for what the problem defines / tells you.
-- In the 2nd sentence, it tells you she bikes at a rate of 7 m/s. So, the 7 in the inequality is the speed biking
-- 3rd sentence tells you: R = number of seconds running
-- 3rd sentence tells you: B = number of seconds biking

So, the problem has told you about 3 out of the 5 items in the inequality.
It didn't tell you what "3" in the "3R" represents. And, it didn't tell you what "1000" represents.
Hint: one is how fast she runs and the other is the distance she wants to cover.
Which number goes with each item? What do you think?
Comment back if you get stuck.