Solving Equations In Algebra - The BasicsLearning solving equations is a significant step in your child's mathematical career. If learned properly early on your child will have the best chance of success in this important subject.
What Is An Equation?An algebra equation is different to a regular math equation. In a regular problem, all the numbers are given and the task is to find the answer. An algebra equation, on the other hand, gives you the answer, but is missing one of the parts of the question. Look at the figure to the right: on top is a regular equation, and beneath it is an algebra equation of roughly the same difficulty. We should already be familiar with the use of order of operations, also called BODMAS, for solving math problems. If your child is not already familiar with this, it is necessary to practice that skill first. To solve complex equations we will need to employ BODMAS once again, but this time in reverse.
The Name Of The LetterThe letter is called either the variable or the unknown and it can be any letter or symbol. Very often it is the letter x which causes great confusion as children confuse this with the multiplication sign. The image to the right shows several simple equations with the letter, or variable, highlighted in red. Getting The Letter By Itself The goal of algebra equation solving is to have the letter by itself on one side of the equals sign. It does not matter which side it is on since they are both equal, but we commonly see the letter ending up on the left side of the equals sign. In order to achieve this, we need to remove all the things that are attached to the letter. We achieve this by using the same number but opposite sign. We remember that anything that happens on one side of the = sign must also be done on the other side or it is no longer equal. Traditionally, the easiest way to do this is to write the thing you need to do under the sum, then do it. Take a look at the following examples. Example 1: Here there is a +4 on the same side of the = sign as the letter.
This needs to be removed. We ask "What is the opposite of plus four?" to which the answer is "Take away four". We write this -4 under BOTH the +4 on the left side of the = sign and under the 9 on the right side of the = sign.
Now the +4 and the -4 on the left of the = sign cancel each other out; that is the point of doing it. On the right side we now do the sum as it is given. The bottom number is subtracted from the top one.
Finally we end up with the letter on one side and a mumber on the other. The problem is solved.
That's A Bit Tedious Indeed it is, but this process of solving equations is quickly learned this way and children will soon start shortening it and speeding up their work. Example 2: This sum involves a -5 with the letter. The opposite of this is +5. All the steps are shown below:
Example 3: This letter is divided by 3. To undo division by 3, we need to multiply by 3 on both sides of the = sign:
Example 4: This one has the number in front of the letter. This means "multiplied by". It is useful when solving equations if you can imagine seeing a little multiplication sign between the number and the letter. Clearly the opposite of multiplication is division. So once again we use the same number but the opposite operation.
Practice The Skill Understanding the concept of solving equations in algebra is a good start, but it is repetitio that reinforces the concept and forms it into a skill. Please feel free to download, save and use this one step equations algebra sheet. I have found this degree of repetition effective in developing students' skills with this basic idea. The answers for this sheet can be arrived at by simple mental math, but it is important to follow the solving equations method of writing the necessary opposite operation underneath the equation, and on both sides of the = sign. This will come into use later on. If you found this information useful, please share this site with others on your blog or website. Return from Solving Equations to Algebra Help or return to the Green Planet home page for Solar Power Facts.
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