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Solving Equations

Solving equations is the very beginning of being able to do algebra. Solving equations usually starts in a primary grade, like 1st, 2nd, or 3rd and goes through high school. The basic idea behind solving equations is to be able to find the missing number. In this section, we’re going to start out with the very basics of solving equations, and move on to some harder stuff.

Find the Missing Number

The first major step is to be able to find a missing number. This means that you need to be familiar with your addition, subtraction, multiplication, and division facts. Try a few of the following:

There are two different ways to think about this; you should go with whichever one comes more naturally. You can either start at 5 and count up to 8—the amount you count up is your answer, or, you can subtract 8 – 5, and that number is your answer.

In detail—the first method would involve counting up. That means you start with 5. You’re counting up to 8. So, you already have 5, you say “6, 7, 8.” Three numbers, so your answer is 3.

The second method, in detail, would involve subtraction. You would take the number after the equals sign (8) and subtract the number before the equals sign (5) in order to get 3.

When you first saw the problem, you probably thought of the answer right away in your head, and if you stop and think about it, chances are you used one of the above listed methods. Whichever way came to you first is the way you’ll want to think about it!

Let's try another one:

This one probably also popped into your head right away. There are also two different ways to think about this one.

The first method would be to think about what number plus 5 = 9. You would think that 4 + 5 = 9, so your answer would be 4.

The second method would be to switch, in your head, the 5 and the question mark, and think about 9 – 5, which gives you 4.

One last example, and then you can practice on your own.

There are, as you may have guessed, also two ways to think about solving this problem. The first way you can think about it is what number minus 3 = 2? If you know your subtraction facts, you’ll think that 5 – 3 = 2, and thus your answer is 5.

The other way you can think about it is 3 + 2 = ? We know that if we add 3 and 2 together, we’ll get 5. Thus, our answer to the problem is 5.

Now, here are a few for you to try on your own. When you think you have the answer, type it into the box and check your answer with ours!

Think to yourself, "4 plus what = 6?" The answer: 2.

2

Think to yourself, "What minus 5 = 10?", or "10 + 5 = what?" The answer: 15.

15

Think to yourself, "7 minus what = 5?" The answer: 2.

2

Think to yourself, "What plus 8 = 15?" The answer: 7.

7

Think to yourself, "What minus 3 = 5?" or "5 + 3 = what?" The answer: 8.

8