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### Course: Pre-algebra>Unit 7

Lesson 7: Intro to inequalities with variables

# Testing solutions to inequalities

Inequalities are like puzzles where you compare two things. You can solve these puzzles by trying different numbers and seeing which ones make the puzzle true. Some numbers will work for one puzzle but not for another. It's all about finding the right fit!

## Want to join the conversation?

• is it possible for there to be a negative X?
(43 votes)
• yes x can be any value rational or irrational.
(25 votes)
• How did he get the numbers 0 1 2 5?
(6 votes)
• There is no magic. You can pick any number you want and test it to see if it is a solution to the inequality. Sal just happened to select: 0, 1, 2, and 5.
(35 votes)
• I don't under stand this at all
(8 votes)
• If you have no trouble solving for regular equations you shouldn't let inequalities scare you away. They may seem confusing but if you learn what the symbols represent and learn to recognize inequalities than you will be fine.

Dont stress it.
Take breaks and if anything repeat what Sal says a loud to yourself. That helps me a lot to understand and listen to what is going on.
(30 votes)
• Sal kinda lost me at the number two... Because he says 2+2 < 2
*2 even tho it would be 4 < 4 which he says is correct but then,when it comes to 3*2+4 > 5*2 which would be 10 > 10 the answer is incorrect-...Why?
(11 votes)
• In the first one, the inequality is "less than OR equal to". Since 4=4, the inequality is true.

In the 2nd one, the inequality is "greater than". Since 10 is not greater than 10, it is false.

Hope this helps.
(17 votes)
• why is it possible for an x to be negative
(8 votes)
• yes x can be any number so it could be -1000 if you want it to
(20 votes)
• Can you guys help me solve this 2x2+3+4x
(11 votes)
• If the x in between the 2's represents multiplication, then this is the answer.

(1.) 2 * 2 + 3 + 4x (Multiplication comes first)
(2.) 4 + 3 + 4x (Now the addition)
(3.) 7 + 4x (This is the final answer because no like terms remain.)
(12 votes)
• At don't you have to mutiply 2x2
(10 votes)
• Also, the way you have written it out makes it look like two times two, which would equal 4...
(9 votes)
• this is too hard to understand
(7 votes)
• Try to watch many videos and do every question with the video. It helps.
(11 votes)
• What is math for anyway because its useless
(0 votes)
• Without math, you wouldn't have many things that you enjoy or need in life.
No video games
No tv
No smartphone
No sports
No buildings that are structurally sound
No medical treatments to keep you well
No ability to manage money

Math is used in many real life things. You may not like math, but you need to know math and how it relates to real life.
(29 votes)
• what is the point of greater or equal to or less than a equal to signs?
(7 votes)
• We can't take the square root of a negative number and expect to get a real output. Therefore we can say that 'x' must be greater than or equal to 0, if we want to take the square root of x.
(5 votes)

## Video transcript

- [Voiceover] We have two inequalities here, the first one says that x plus two is less than or equal to two x. This one over here in I guess this light-purple-mauve color, is three x plus four is greater than five x. Over here we have four numbers and what I want to do in this video is test whether any of these four numbers satisfy either of these inequalities. I encourage you to pause this video and try these numbers out, does zero satisfy this inequality? Does it satisfy this one? Does one satisfy this one? Does it satisfy that one? I encourage you to try these four numbers out on these two inequalities. Assuming you have tried that, let's work through this together. Let's say, if we try out zero on this inequality right over here, let's substitute x with zero. So, we'll have zero plus two needs to be less than or equal to two times zero. Is that true? Well, on the left hand side, this is two needs to be less than or equal to zero. Is that true, is two less than or equal to zero? No, two is larger than zero. So this is not going to be true, this does not satisfy the left hand side inequality, let's see if it satisfies this inequality over here. In order to satisfy it, three times zero plus four needs to be greater than five times zero. Well three times zero is just zero, five times zero is zero. So four needs to be greater than zero, which is true. So it does satisfy this inequality right over here so zero does satisfy this inequality. Let's try out one. To satisfy this one, one plus two needs to be less than or equal to two. One plus two is three, is three less than or equal than two? No, three is larger than two. This does not satisfy the left hand inequality. What about the right hand inequality right over here? Three times one plus four needs to be greater than five times one. So three times one is three, plus four. So seven needs to be greater than five, well that's true. Both zero and one satisfy three x plus four is greater than five x, neither of them satisfy x plus two is less than or equal to two x. Now let's go to the two. I know it's getting a little bit unaligned, but I'll just do it all in the same color so you can tell. Let's try out two here, two plus two needs to be less than or equal to two times two. Four needs to be less than or equal to four. Well four is equal to four and it just has to be less than or equal, so this satisfies. This satisfies this inequality. What about this purple inequality? Let's see, three times two plus four needs to be greater than five times two. Three times two is six plus four is ten, needs to be greater than 10. 10 is equal to 10, it's not greater than 10. It does not satisfy this inequality. If this was a greater than or equal to it would have satisfied but it's not. 10 is not greater than 10. It would satisfy greater than or equal to because 10 is equal to 10. So two satisfies the left hand one but not the right hand one. Let's try out five. Five plus two needs to be less than or equal to two times five, once again everywhere we see an x, we replace it with a five. Seven needs to be less than or equal to 10. Which is absolutely true, seven is less than 10. So it satisfies less than or equal to. Five satisfies this inequality and what you're probably noticing now is that an inequality can have many numbers that satisfy. In fact they sometimes will have nothing that satisfies it and sometimes they might have an infinite number of numbers that satisfy it and you see that right over here. We're just testing out a few numbers. For this left one, zero and one didn't work, two and five did work. This right one, zero and one worked, two didn't work. Let's see what five does. In order for five to satisfy it, three times x. Now we're gonna try x being five. Three times five plus four needs to be greater than five times five. Three times five is fifteen, fifteen plus four is nineteen. Nineteen is to be greater than 25, it is not. So five does not satisfy this inequality right over here. Anyway, hopefully you found that fun.