Solving an equation and finding the value of the variable requires "undoing" what has been done to the variable. We do this by using inverse operations to isolate the variable. Remember that an equation is two expressions that are equal to each other. This means that when using inverse operations to isolate the variable, what is done to one side of the equation has to be done to the other side as well so that the equation stays balanced. For example, if the variable is being divided by 5, then to isolate the variable, do the opposite operation, which is multiplying by 5. What you do to one side, you have to do to the other, so make sure to multiply both sides by 5. After solving for the variable, check your answer by plugging the value into the original equation. If the equation is true -- meaning the left side of the equation equals the right side of the equation -- then the solution is correct.
A more difficult problem that you might see in your solving equations homework is something that looks like this because it has x is involved as part of a fraction. Notice how x is in the numerator which means the top of the fraction.
So a lot of students that I see will go right ahead and say x equals 3 and they'll say I'm done, problem solved, move on. However, that is not the right answer, 3 divided by 5 is not equal to 15. So whoever writes this is on the right track because 5 and 3 have something to do with 15. They're thinking along the right lines like multiplying, dividing however that's not the right answer, 3 divided by 5 is not equal to 15, 3 times 5 that equals 15.
So in order to do this problem correctly what you need to do is undo what's been going on to x, like x is being divided by 5. I need to undo that dividing and the way to undo dividing is to do the opposite which is multiplying so I'm going to multiply both sides by 5.
Now that was clever because my 5/5 becomes a giant 1 to cancel out and I'm left with x equals whatever 15 times 5 is. If you're not sure do it the old school way. I personally off top of my head don't know what that is, so x equals 75. That's my solution and it makes more sense than 3. Like if I were to say 3 divided by 5 equals 15, no. But 75 divided by 5 is probably equal to 15. Let's do a check just to make your teacher happy and follow the directions of the problem because it says check your solution.
We want to make sure that 75 divided by 5 is indeed 15, so you can write it out like this and just make sure that when you do all this problem, you do in fact get the answer 15.
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