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### Course: Algebra (all content) > Unit 6

Lesson 4: Modeling with linear inequalities- Writing two-variable inequalities word problem
- Interpreting two-variable inequalities word problem
- Solving two-variable inequalities word problem
- Graphs of two-variable inequalities word problem
- Two-variable inequalities word problems
- Modeling with systems of inequalities
- Writing systems of inequalities word problem
- Solving systems of inequalities word problem
- Graphs of systems of inequalities word problem
- Systems of inequalities word problems
- Analyzing structure with linear inequalities: fruits
- Analyzing structure with linear inequalities: balls
- Analyzing structure with linear inequalities

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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?

- At2:17Sal 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.(14 votes)
- Whenever you multiply or divide by a negative number on both sides, you have to flip the inequality sign. Sal talks about it here:

https://www.khanacademy.org/math/algebra/linear_inequalities/inequalities/v/inequalities-using-multiplication-and-division

I hope that helps.(31 votes)

- 3:22Couldn'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?(6 votes)
- 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.(10 votes)

- How to write an inequality when its says "
**At most**" and when it says "**At least**"?(2 votes)- 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.(8 votes)

- at around3:41Sal 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?(3 votes)
- Well, flipping 7/10 to 10/7 to multiply the equations is called multiplying by the reciprocal or inverse (of the fraction). 10/7 is the reciprocal or inverse of 7/10. So there actually is a name for it.

Here are two videos to help you understand it better: ♪https://www.khanacademy.org/math/arithmetic/fraction-arithmetic/arith-review-dividing-fractions/v/conceptual-understanding-of-dividing-fractions-by-fractions

♪https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-algebra-arithmetic-properties/v/inverse-property-of-multiplication

I hope this helps :D.(4 votes)

- Why are you using fractions and not decimals? I was surprised to see that. I did 6/0.7 = 8.6 as the answer.(2 votes)
- 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.(6 votes)

- i'm still confused is there a way this can be explained better to me(3 votes)
- What does it mean when the line is dotted, and what does it mean when it is not dotted?(1 vote)
- It is a matter of whether or not points on the line count as part of the solution. So if it is dashed or dotted, these points do not count and you should see a (< or >) inequality symbol. Greater than or less than does not include the number. If it is solid, you are dealing with ≥ or ≤ where all the points on the line are part of the solution (greater than or equal to).(4 votes)

- 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? "(0 votes)- 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.(5 votes)

- at2:50would just dividing 0.7/6 be wrong(1 vote)
- Yes, that would be incorrect.

You need to divide both sides by 0.7.

6 divided by 0.7 = 6/0.7

Your version is 0.7 divided by 6, which is like say 2/4 is the same as 4/2. You get completely different results.

Hope this helps.(1 vote)

## Video transcript

- Ezra enjoys gardening. Every sunflower plant he waters requires 0.7 liters of water, and every lily plant he waters requires 0.5 liters of water. Ezra has a total of 11 liters
of water for these plants. In the following inequality, S represents the number
of sunflower plants and L represents the number of lily plants Ezra can water. See if this makes sense. So it looks like... So the number of sunflower plants is S and he would have to use
7/10 of a liter per plant. So this first term right over here, this is how much water used to water the sunflower plants and then the second term is how much water used to water the lily plants cause he needs half a liter
for each of the L lily plants. And he has a total of 11 liters. So the sum right over here has to be less than or equal to 11. Alright. Ezra waters 10 lily plants. So that's L is equal to 10. How many sunflower plants
can he water at most with the remaining amount of water? Well let's think about this a little bit. We have 0.7, 0.7 times the number of
sunflower plants he waters. Plus, plus... So we're gonna assume L is equal to 10. He waters 10 lily plants and each of them, he
gives half a liter to. So 0.5, 0.5 x 10 is going to be 5. So it's gonna be five liters,
watering the 10 lily plants and this has to be less
than or equal to 11. So we can try to isolate
the S on the left hand side. So let's, let's do that.
The number of sunflowers. So we could first subtract
five from both sides. Subtract five from both sides. and we are going to be left with... We are going to be left
with on the left hand side, we're gonna just have 0.7 x S So this expression is
the total amount of water he's gonna spend on the sunflower plants has to be less than or equal to 11- 5 is equal to six. And so now, we can
divide both sides by 0.7 And we're gonna have to
change the inequality because we are diving by
a positive number, 0.7 So we're gonna get S... S is less than or equal to 6 ÷ 0.7 or we could even write this as... we could write this as, well... This is 6 divided by 0.7 Let me write everything as a fraction. This is the same thing as 6 ÷ 7/10 which is equal to six times 10 over seven which is equal to 60/7 which is equal to what is this? 8 4/7 so S has to be less than
eight and four sevenths. Now assuming that he's only, we're only thinking in
terms of whole plants... (mumbles) integer numbers but actually
whole numbers of plants and so, if S has to be less than 8 4/7, how many sunflower plants can he water at most with the
remaining amount of water? Well, we'll say that he had, most he can water eight plants. We're gonna assume that he can't water just a fraction of a plant. He either waters something or he doesn't. So he's gonna water eight, he is gonna water eight plants. Cause that's the largest whole number that is less than 8 4/7. That satisfies... That is less than or equal
to 8 4/7 I should say.