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Steps For Solving Equations4/16/2021
The exact same methods work with both variables and numbers.Linear equations are the simplest equations that youll deal with.
Back in your early years, when you were learning addition, your teacher probably gave you worksheets to complete that had exercises like the following. However, since were older now than when we were filling in boxes, the equations can also be much more complicated, and therefore the methods well use to solve the equations will be a bit more advanced. We do this in order to get the variable by itself; in technical terms, we are isolating the variable. This results in the equation being rearranged to say (variable) equals (some number), where (some number) is the answer theyre looking for. To solve this equation, I need to get the x by itself; that is, I need to get x on one side of the equals sign, and some number on the other side. Since the 6 is added to the x, I need to subtract this 6 to get rid of it. That is, I will need to subtract a 6 from the x in order to undo their having added a 6 to it. Since I want to get x by itself, I dont like the 3 thats currently subtracted from it. The opposite of subtraction is addition, so Ill undo the subtract 3 by adding 3 to both sides of the equation, and then adding down to simplify to get my answer. To do this checking, you need only plug your answer into the original equation, and make sure that you end up with a true statement. This is, after all, the definition of the solution to an equation; namely, the solution is any value, or set of values for more complicated equations, later on, which makes the original equation a true statement.). Thats okay; it doesnt matter where the variable is, as long as I get isolate it (that is, as long as I can get it by itself on one side of the equals sign). To undo the subtraction, Ill add three to either side of the equation. Thats why I carried down only the x on the right-hand side.). Steps For Solving Equations Full Credit OnIve made sure to label things clearly, so the grader is able to find my check (so Ill get full credit on the exercise). ![]() When youre solving, the variable will end up wherever it ends up. When youre writing out the solution, the variable goes on the left. But not quite. I dont have plain old x on the right-hand side; instead, Ive got x. So what would happen if I added x to each side of the equation. And this has also converted the original equation into a simple one-step equation. Ill get rid of the 2 from the left-hand side by subtracting it over to the right-hand side. If the negative of the variable equalled a positive two, then the positive of the variable should equal a negative two. The important thing to notice is that you can add and subtract variables to the other side of an equation, just like you can add and subtract numbers to the other side.
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