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Solving an equation in algebra usually means finding out what the variable is. Algebra equations are usually set up with numbers and/or variables on both sides, like this: x + 2 = 9 4. To figure out what the variable is, you need to get it by itself on one side of the equals sign. Whatever is left on the other side of the equals sign is your answer. In the example (x + 2 = 9 4), to get x by itself on the left side of the equation, we need to get rid of the "+ 2". To do this, we'll simply subtract 2 from that side, leaving us with x = 9 4. However, to keep both sides of the equation equal, we also need to subtract 2 from the other side. This leaves us with x = 9 4 - 2. Following the order of operations, we multiply first, then subtract, giving us an answer of x = 36 - 2 = 34. As we just saw above, getting x by itself on one side of the equals sign usually means getting rid of the numbers next to it. To do this, we perform the "opposite" operation on both sides of the equation. For instance, in the equation x + 3 = 0, since we see a "+ 3" next to our x, we'll put a "- 3" on both sides. The "+ 3" and "- 3", leaving x by itself and "-3" on the other side of the equals sign, like this: x = -3. In general, addition and subtraction are like "opposites" do one to get rid of the other. See below: For addition, subtract. Example: x + 9 = 3 x = 3 - 9 For subtraction, add. Example: x - 4 = 20 x = 20 + 4 Multiplication and division are a little harder to work with than addition and subtraction, but they have the same "opposite" relationship. If you see a " 3" on one side, you'll cancel it by dividing both sides by 3, and so on. With multiplication and division, you must perform the opposite operation on everything on the other side of the equals sign, even if it's more than one number. See below: For multiplication, divide. Example: 6x = 14 + 2 x = (14 + 2)/6 For division, multiply. Example: x/5 = 25 x = 25 5 Exponents are a fairly advanced pre-algebra topic if you don't know how to do them, see our basic exponent article for more information. The "opposite" of an exponent is the root that has the same number as it. For example, the opposite of the 2 exponent is a square root (), the opposite of the 3 exponent is the cube root (3), and so on. It may be a little confusing, but, in these cases, you take the root of both sides when dealing with an exponent. On the other hand, you take the exponent of both sides when you're dealing with a root. See below: For exponents, take the root. Example: x2 = 49 x = 49 For roots, take the exponent. Example: x = 12 x = 122
Try to get the variable by itself in algebra equations. Cancel addition with subtraction (and vice versa). Cancel multiplication with division (and vice versa). Cancel exponents by taking the root (and vice versa).