Solving two-step equations | Linear equations | Algebra I | Khan Academy

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In front of you a bunch of things, You have left scales Unknown masses, indicated by the variable x in blue, In addition to a number of other blocks with a weight of 1 kg each. In particular, you only have 2 of them. You are required to find the value of the variable x, but before you start the solution, I want you Think of a solution using math equations. It may help you in representing your information. For example, it is: Achieve equality between the two quantities on the palm scales. Now, notice what you have on the left cuff You have 3 x blocks, and you can say you have 3 x, You also have two blocks, each with a weight of 1 kg. Write down 2 If as a way to represent what you have on the left side, write the following 3x + 2 Which indicates 3 blocks, each with a weight of x plus 2 kg. This equation represents exactly the one on the left scales. Now, notice what you have on the other side, You can count what is there easily The number is 14 pieces. 14 pieces weighing 1 kg each, so the total weight is 14 kg. And note that the two palm scales are equal. There is no advantage in favor of one hand over another. This means that the total weight in the left cuff must be equal to the weight in the right cuff 14 kg Since the two palm scales are equal, you can write the equal sign = I will write it in white. Now think about the solution and find the value of x, Depending on either the symbols in the handling, or the formal representation in the scale, Think about the following points: How do you get rid of these small pieces weighing 1 kg from the left cuff? I will give you a second thought .. Well: the easiest way to do this is: To remove it from the left cuff, But remember, when you pull it out from the left cuff, Knowing in advance that the two shoulders are equal from the start, the left cuff will become lighter It will go up. So you have to keep your shoulders tied The left cuff is equal to the right cuff. If you delete two pieces of the left cuff, you should delete two pieces of the right cuff as well. Two pieces of the right cuff, and two pieces of the right cuff. What you have done can be expressed mathematically Subtracting the number 2 from both ends of the dependency. Now you have the left side of the equation: 3x + 2, minus 2 The rest is equal to 3x On the right cuff there are 14 pieces, remove two of them It remains 12 pieces. You see what I did. What I deleted and what remained on the two rests. You have 3 left blue pieces left in the left cuff. So what you have done is delete the same amount of the two shoulders. Now you keep the two scales equal to the scale, and you get the equation 3x = 12 And now you have another problem Which is how you can get one value of the variable x, On the left side of the scale, With the necessity of keeping the two scales equal. The easiest way to do this is: If you want one value from the variable, that value is equal to a third of the total value of 3x, What would you get if you multiplied the left side by 1/3 the third, But you have to multiply the right side by the same value, to maintain the equalizer of the shoulders. You can do this mathematically by: Multiply both sides of the equality by 1/3 And I stress the need to hit the two parties by the same value to maintain balance. What you’re doing means exactly keeping a third of your original amount. Delete two blue squares on the left cuff, If you want to get a third of the total number of them. On the left side, you have 12 pieces. You should delete 4 of them. Let me remove everything but four. (Therefore, remove those, and those …) You have 4. I will shade what I have left in the shoulders, Left square one X weight, And in the right cuff 3 squares, each of 1 kg. Mathematically, 1/3 times 3x, Or 3x division 3. Both methods are correct. The remainder on the left side is x And at the right side is 4. By this, you will have maintained a state of balance, by performing the same process on both sides. Notice, then, that one blue block is equal to 4 small blocks, each weighing 1 kg, That is: x = 4 kg

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