[MUSIC] An expression can refer to a single term such as 3b. But, however, more often an expression refers to the sum or difference of two or more terms. Like for example 8x + 9. z- 1/3 y or 18.4t- 1. What makes the difference between an expression and an equation? Is that an expression does not contain an equal sign. An equation refers to two expression that are equal to one another, such as x + 5 = 9. Each equation has a left-hand side, which in our case is x + 5 and a right-hand side which in our case is 9. A solution to an equation is the number that can be substituted in place of the variable, and that makes the equation true. X = 4 is the solution to our equation. In fact if we substitute 4 instead of x, we have got 4 + 5 = 9. Therefore the resulting equation is true. The general rule Is that to solve a basic equation for the unknown, we need to manipulate it. So that all terms with the variable are on the one side of the equation and all terms with the only numbers are on the other side of the equation. According to the addition rule, the same number or term may be added or subtracted on both sides of the equation. According to the multiplication rule, both sides of an equation maybe multiplied or divided by the same non-zero number or term. For example, in order to solve x- 9 = 15 for the unknown, we need to take some steps. Firstly, the variable x must be isolated on the one side of the equation, and the numbers must be located on the opposite sides. How to do that? First of all we need to get rid of 9 and move the 9 to the other side of the equation by adding 9 to both sides. And then we have x-9+9=15+9, which is x+0=24. Thus the solution is x=24. Is this true? Let's confirm that the value of the unknown variable is 24. We just need to substitute 24 for x in the original equation. The original equation was x-9=15. By substituting our solution we get 24-9=15. Therefore our solution x=24 is correct because it's 15=15. Another example, in order to solve k + 7 = 18. Firstly, the variable k must be isolated to the one side of the equation and the numbers must be located on the opposite side. In order to isolate k on the left-hand side, we need to get rid of 7. And then in this case we need to do the opposite of adding 7, which is subtracting 7 from both sides. Then we have that k + 7 = 18. k+7-7=18-7. And then our solution is k=11. Let's go for another example. And let's solve 5p = 60. The term 5p indicates that multiplication of 5 and p, 5p = 60. And then in that case, in order to isolate our variable which is p, on the one side of the equation in the number, on the other side of the equation, we need to get rid of 5. We can do it just by applying the operation which is the inverse of the multiplication that is the division. Therefore, we solve the equation by dividing both sides by 5. And then we have 5p/5 = 60/5. And our solution is p = 12. Another example, involves solving y/3 = 9. The first term indicates y/3. In this case, in order to isolate our variable, that is y, on the one side of the equation and the number on the other side of the equation. We need to get 3 over 3. We can do it just by applying the operation which is inverse of the division, that is the multiplication. Therefore we solve the equation by multiplying both sides by 3 and then we have 3 x y/3 = 9 x 3. And then our solution is y = 27. [MUSIC]
