Basic Rules To Solve Equations - Addition Rule And Multiplication Rule How To Solve for Equations скачать в хорошем качестве

Basic Rules To Solve Equations - Addition Rule And Multiplication Rule How To Solve for Equations

In this video we discuss the basic rules to solve equations. We cover the addition and multiplication rules, going through examples of how to solve basic equations. Transcript/notes When we want to solve basic equations, such as x plus 4 equals 12 or 5z equals 30, there are 2 basic things we need to do. First is change the equation so that all the terms with a variable are on one side of the equation, and second is to get all terms with only numbers on the other side of the equation. There are 2 rules that help us to do this, the addition rule, and the multiplication rule. The addition rule is that the same number or term can be added or subtracted to both sides of an equation. For instance, in the equation x plus 4 equals 12. We have a left side of x plus 4 and a right side of 12. We can add or subtract any same number from both sides of the equation. So, we could add 15 to both sides of the equation, and doing that, the equation would now be x plus 4 plus 15 equals 12 plus 15, which would give us x plus 19 equals 27. But, adding 15 did not help us to achieve the 2 basic things we want to do, get the variable or variables on one side of the equation and get numbers on the other side of the equation. So, in our original equation of x plus 4 equals 12, if we subtract 4 from each side, that will get the x variable by itself on the left side of the equation. So, in doing that, we have x plus 4 minus 4 equals 12 minus 4. Doing the operation, we have x plus zero equals 8, which gives us a final answer of x equals 8. Next, we can check our solution. We plug the value of x equals 8 into the original equation, 8 plus 4 equals 12, and 12 equals 12, so our solution checks out. This also works for adding to both sides when necessary. For instance z minus 14 equals 32. To get the variable z alone on the left side, we need to add 14, so we will add 14 to each side, and going through the process we get z equals 46. Next, we check our solution, which I have done on the screen, and the solution checks out. Now for the multiplication rule. The multiplication rule is that both sides of an equation can be multiplied or divided by the same nonzero number or term. For instance, in the equation 5z equals 30. We have a left side of 5z and a right side of 30. We can multiply or divide by any same number for both sides of the equation. We could divide both sides by 7, and doing that, the equation would now be 5z divided by, or 5z over 7 equals 30 divided by, or 30 over 7. But, dividing both sides by 7 did not help us to achieve the 2 basic things we want to do, get the variable or variables on one side of the equation and get numbers on the other side of the equation. So, in our original equation of 5z equals 30, if we divide both sides by 5, that will get the z variable by itself on the left side of the equation. So, in doing that, we have 5z over 5 equals 30 over 5. Doing the operation, 5 over 5 is 1, so, we have 1z or just z on the left side and 30 over 5 equals 6 on the right side, which gives us a final answer of z equals 6. Again, we can check our solution by plugging the value of z equals 6 into the original equation. 5 times 6 equals 30, and 30 equals 30, so, the solution checks out. This also works for multiplying both sides of the equation when necessary. For instance, 1 over 6 t equals 4. To get the variable t alone on the left side of the equation we can multiply by 6. So, we will multiply both sides by 6. The 6’s on the left side cancel out and 4 times 6 equals 24. Now we have 1t, or just t equals 24 as our solution. Next we check the solution by plugging 24 in for t in the original equation, and we get 4 equals 4, so our solution checks out. Here are a few more examples on the screen for you, and remember, the key to solving equations is to get the variable on one side and numbers on the other side. Timestamps 0:00 2 key things to do to solve equations 0:23 Addition rule explained 1:51 Multiplication rule explained 3:38 More example problems