An equation is simply a way of saying that two things are equal to each other. If I were to give you the following equation:
___ + 6 = 13
You could probably tell me right away that the number that goes in the blank should be 7.
When we work with algebraic concepts, we don't use blanks, we use letters. Usually, we use the letters x or y, but any letter will do. So I can write the same equation like this:
x + 6 = 13
This may still seem like an easy concept, because you know what number plus 6 equals 13. However, the process you are using in your head looks should look something like this:
___ + 6 = 13
You could probably tell me right away that the number that goes in the blank should be 7.
When we work with algebraic concepts, we don't use blanks, we use letters. Usually, we use the letters x or y, but any letter will do. So I can write the same equation like this:
x + 6 = 13
This may still seem like an easy concept, because you know what number plus 6 equals 13. However, the process you are using in your head looks should look something like this:
x + 6 = 13
x + 6 - 6 = 13 -6 x + 0 = 7 x = 7 |
The first step is always to write out your equation so that you will have plenty of room to solve.
You want to get rid of the "+ 6" so you have to do the opposite, which is subtracting 6. When we do something to one side of the equation, we always have to do it to the other side as well. When we take away the "+6" we are left with a "+ 0", which means that nothing will be added to that side. This gets the "x" by itself, which is what we want. |
When you are working on solving an equation and want to get part of that equation out of the way, remember to use the opposite operation on both sides of the equation:
If you have "3x" and want to get "x" by itself, you have to divide both sides of the equation by 3.
If you have "x/4" and want to get "x" by itself, you have to multiply both side of the equation by 4.
If you have "x + 6" and want to get "x" by itself, you have to subtract 6 from both sides of the equation.
If you have "x - 8" and want to get "x" by itself, you have to add 8 to both sides of the equation.
If you have "3x" and want to get "x" by itself, you have to divide both sides of the equation by 3.
If you have "x/4" and want to get "x" by itself, you have to multiply both side of the equation by 4.
If you have "x + 6" and want to get "x" by itself, you have to subtract 6 from both sides of the equation.
If you have "x - 8" and want to get "x" by itself, you have to add 8 to both sides of the equation.
Writing an equation from a picture
To write an equation from a graphic, use the different shapes to determine what you should use for your variable. Usually, the variable will be visible inside the graphic that is used to represent it, such as the triangles above. However, if not, simply assign a letter to the shape that you feel represents the variable.
Round shapes usually will represent "1" whole in the picture. So in the above picture, we have 3 triangles and 4 circles on the left and 1 triangle and 12 circles on the right. These are already seperated by an equal sign but you might also see them on a set of balance scales in some pictures.
To write out an equation, break the picture down into two sides, seperated by an equal sign:
___________ = ___________
Then figure up your left side of the equation. In this instance, we have 3 triangles on the left, which are represented by "x", so I have "3x." I also have 4 circles, which represent units or ones, so I have 4 positive ones or "+4." Altogether this looks like "3x + 4." That is what I will place on the left side of my equation:
3x + 4 = ____________
On the right side of my equation, I have 1 triangle that represents the letter "x" so I only have "1x." I have 12 circles that represent units or ones, so I have 12 positive ones or "+12." Altogether this looks like "1x + 12." That is what I will place on the right side of my equation:
3x + 4 = 1x + 12
Now that I have written my equation, I can use the rules in the solving section above to solve for the answer.
Round shapes usually will represent "1" whole in the picture. So in the above picture, we have 3 triangles and 4 circles on the left and 1 triangle and 12 circles on the right. These are already seperated by an equal sign but you might also see them on a set of balance scales in some pictures.
To write out an equation, break the picture down into two sides, seperated by an equal sign:
___________ = ___________
Then figure up your left side of the equation. In this instance, we have 3 triangles on the left, which are represented by "x", so I have "3x." I also have 4 circles, which represent units or ones, so I have 4 positive ones or "+4." Altogether this looks like "3x + 4." That is what I will place on the left side of my equation:
3x + 4 = ____________
On the right side of my equation, I have 1 triangle that represents the letter "x" so I only have "1x." I have 12 circles that represent units or ones, so I have 12 positive ones or "+12." Altogether this looks like "1x + 12." That is what I will place on the right side of my equation:
3x + 4 = 1x + 12
Now that I have written my equation, I can use the rules in the solving section above to solve for the answer.
3x + 4 = 1x + 12
3x + 4 -4 = 1x + 12 - 4 3x = 1x +8 3x - 1x = 1x - 1x +8 2x = 8 2x/2 = 8/2 x = 4 |
My first step is to write my equation so that I have plenty of room to solve.
My next step is to get all of my units on one side and all of my variables, or "x"s on the other. I will work with units first and try to get them to the right side. I had a "+4" on the left side of my equation so I will use the opposite operation and subtract 4 from both sides. To make sure I have everything straight before I start my next step, I rewrite my equation. I next want to get all of my variables on the left side. I have a positive 1x on the right side that I want to get rid off, so I will use the opposite operation and subtract 1x from both sides of the equation. Again, I rewrite my new equation before starting my next step. I now want to get just 1x on one side of my equation. To do that, I will have to get rid of the 2 in front of the "x". Since I am multiplying 2 times x, I will use the opposite operation to get rid of the 2 and divide both sides of the equation by 2. All I am left with at this point should be my answer, so I know that each "x", or each triangle in this case, is worth 4 units or 4 coins. |