Inequality questions blog – mburton

An inequality compares two values, showing if one is less than, greater than, equal to, or not equal to another value. A example of what this looks like(4>3). In this example I am using the greater/less than symbol. Since 4 is greater than 3 the greater/less than simple would be facing with the open part of the arrow shape facing towards the 4. Making it obvious that the 4 is greater than the 3 which is one the less than side of the arrow shaped symbol. Two other examples are (4=4) and (4≠5). The first symbol is the equal symbol and is pretty straight forwards, it just means they are equal to the same number. The second example is the opposite and just means that they do not equal each other. The last two other symbols of inequalities are the same shape as the greater/less than symbols but instead they have a line underneath. Which would look like (4 ≥ x). This symbol can go both ways and it works just like the normal greater/less than symbols, except that the number (x) in my small example can either be a number below 4 or equal to 4.

When graphing inequalities on a number like there are a few things you must do. If there is an unknown number in the equation such as (4>x) then you would have to put arrows point in a direction that would either go right or left on the number line. If you know that (x) is less than 4 from the example than you would draw a circle and than an arrow pointing left down the number line to signify that it is smaller than 4. If it was the other way around and (x) was bigger than 4 than you would put the arrow pointing the other way.

Something else you have to do when graphing inequalities on a number like is making sure that you are drawing the circle from the number point you are writing from is correct. When putting these dots on the graph you have to make sure you are doing the right one. You can either put a hallow circle or a filled in dot. These signify different things with inequality equations. If the equation had the arrow with the line underneath is which looks like ≤ then you would have to put a filled in dot. That tells you that the unknown number can be equal to the number that the dot is located on or wherever the direction the arrow is pointing to. If you have the normal greater/less than symbol in your equation, which look like <, then you would put a hallow circle meaning the unknown number can only be wherever the direction of the pointing arrow is going on the graph.

When it comes to inequalities some of the time it can be quite straight forward, although where other times it is hard to make out what to do first. It is just like the last unit when working with the equal sign that is in the middle of the two equations. When simplifying the question you must take away the same amount from each side so it is a legal move and will still work in the question. When simplifying you want to get it as small and easier to solve as you go along and  an ideal way to simplify it is to do step by step to make it as small as possible. Such as to have the unknown number on one side (x) and the known number on the other side.

To get on your way to solving on of these equations you must use the BFSD tactic. This stands for Brackets, Fractions, Sort, Divide. This tactic works well for me and makes everything a little easier when trying to figure out what to do first when finding a big ugly equation. First, you simplify all the brackets and work with those first just like every other equation. For example, in the equation (2(2x + 3) < 3x – 4) you would simplify the brackets at the beginning of the question so that when you are done that step it will look a little more simple, like this (4x + 6 < 3x – 4).

Once you’ve done that you deal with the fractions, this would be either making all the number in the equation fractions or turning them all into whole numbers. If there were one or more fractions in the equation after you do the first step then you can a choice I would make is to change all the numbers into fractions by perhaps putting a one below it. Like in this equation,                      (2 + 3x > 2/3 – 2x). You would then turn all the numbers into fractions like this (2/1 + 3x/1 > 2/3 – 2x/1). Then you could multiply all the fractions so that all of them have to same denominator, in this equation you would probably want to make the denominators into a (3) since one of the fractions already has that denominator and the rest can fit into that number easily. Which would look like this (6/3 + 9x/3 > 2/3 – 6x/3). Another step you could do with the fractions is that once you make them all the same denominator then you can just get rid of them, kind of like you are hiding them. Or you can just keep it the way that it is and work with fractions if you find that easier for the particular equation. If you got rid of the denominators the equation would look like this (6 + 9x > 2 – 6x). If there are no fractions in the equation or you don’t have to make any fractions than just leave it all alone and skip the step.

After that you would sort, this mean either subtracting or adding the same type of number to one side and another type of number to the other side. For example, in the equation (2x  + 4 > x + 2) you would want to subtract +4 from both side of the equation so that it no longer exists. This would then look like this (2x > x – 2), then you would want only the -2 on one side and the unknown number on the other side. So, you would subtract (x) from both side, getting rid of the (x) on the right of the equation in the example. This would turn out to look like this (x > -2).  Then, after doing all that you finally have a small answer.

In my example you don’t need to divide because there is already only on (x), but if there were say (2x) on one side still then you would have to do the last step which is dividing. To divide all you need to do is divide the amount of (x)s there are on the one side. If there were a (2x) on one side and a 4 on the other you would need to divide each side by 2. Then you would be done the equation and all you would need to do is check it.

There is also something called doing a swap. If you had an equation where once you simplified it all down and did everything correctly but there is a negative on the unknown number. If this happens you would need to swap it so that you would transfer the negative symbol over to the other number on the other side and turn over the more than symbol and that would be it.

When doing equations you should usually check your answers when you are done to make sure you were correct and didn’t make any mistakes while solving. To solve an inequality question you need to know if the unknown umber is larger, equal, or smaller than the known number. For instance, in the equation (4< x) you know that x is larger than 4. A way to check your answer after simplifying the question is to take a any number above 4 and replace x with that number in the equation, if the question is correct and makes sense in the end you solved the equation correctly. If the final answer is not correct and does not make sense then you should go back through your steps and find out where you went wrong so you can fix it.

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