Beginners Algebra | Linear inequalities :Lesson 8 | By LADYMATHS
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Today we will be learning about linear inequalities. This term actually might sound a little bit scary at first but in fact we have been learning about them from primary school maths.Inequalities is basically when you look at two different linear equations and you comparethe two. So you say which one is bigger than,
or which one is equal to, or which one is less than, which one is less than and equal to and which one is greater than and equal to. Let's look at some examples. sometimes we might find that we are given a statement like 3x plus 7 is greater reallthan or equal
to 2x. what does that really mean? It really means that the value of 3x plus 7 is greater than that of the value of 2x. What is we changed the symbol. What if we turned it around to
make it face the other way? This would mean the exact opposite. This would mean that the 2x's value is greater or equal to the value of 3x plus 7. What if we remove the line?
By removing that line we actually are saying that the value of 2x is greater than 3x plus 7 so they are not equal to each other. And if we flip that to the other side, then that means that 3x +7 is greater than 2x and that they are not equal to each other. The easiest
way to really remember this is to think of this symbol, as a mouth. This mouth enjoys eating food. And it usually is quite greedy and it likes to eat the bigger numbers. So for example, if we had an 8 and if we had a 7, the mouth would ignore the 7 and go for
the 8. So it is actually pointing towards the 8. This basically says that the mouth wants to eat up the 8 because it is the bigger value and it will reject the 7 because it is small. Okay, let's look at an example. So, let's say for example we've got 3x + 8
is greater than or equal to x + 3. What we really want to do is we want to simplify this inequality and we do that by first subtracting 8 from both sides. So we are going to go 3x plus 8 minus 8 is bigger than or equal to x plus 3 minus 8. This 8-8 is equal to 0 so
we are going to just have 3x. And here we are going to have x+3-8 is equal to x minus 5. Now we want to subtract x from both sides,
because ultimately we want the x's on one side and the, just the singular numbers on the other side. So we are going to get x minus x minus 5 and 3x-x. These two x's are going to be crossed out and become zero. And we are going to be left with -5 on the right hand side. And then 3x-x is equal to 2x. We
want to figure out what, we want to treat this as if we are figuring out an algebraic equation, so we want to isolate x and keep it on its own. The way to do that is to divide
both sides of the equation by 2. So we want to do 2x divided by 2, -5 divided by 2. These two cross out and we are left with xis greater than or equal to -5 over 2. And that is our answer. If you have any questions regarding the methods that I used in this video, please feel free to leave them below. If you found my little tricks and tips useful, then please like this video and subscribe to this channel for more videos like this. And as always,
Happy studying!
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