Certainly! So you're trying to find x.
8(x - 1) + 3 = 7x - 6 - 5x
Okay, the first thing you should do is distribute the eight to x-1. The right side does not need distribution.
8x - 8 + 3 = 7x - 6 - 5x
Now, the next thing you should do is combine the like terms, and the terms that are different, you seperate them into different sides of the equation. So, for the terms that contain x, I usually put them on the left side of the equation, and for the terms that are normal numbers, I just put them on the right side of the equation. So combine the like terms.
8x - 5 = 2x - 6
You simply just add negative eight to three and 7x to negative 5x. Now, after you have done this, it is time to seperate the different terms to different sides of the equation. In this case, we must subtract both sides of the equation by 2x so that the x terms will remain on the left, and we must add five to both sides so that the number terms will stay on the right. Watch closely.
8x - 2x - 5 = 2x - 2x - 6
6x - 5 = -6
6x - 5 + 5 = -6 + 5
6x = -1
After you have done this, it is time to divide each side so that the x terms will remain as one x. So in this case, we divide both sides by six.
6x/6 = -1/6
x = -1/6
x = -1/6 is your final answer, but we're not done yet. Sometimes in an equation you might want to check that the resultant of the variable, x, when plugged in to the equation, fits perfectly, and checking the equation will make sure your resultant is correct. So, for the equation 8(x - 1) + 3 = 7x - 6 - 5x, we just plug in -1/6 to every x in that equation. Watch closely.
8[(-1/6) - 1] + 3 = 7(-1/6) - 6 - 5(-1/6)
At this point, just use the PEMDAS rule to find that -1/6 is truly x. So like before, you start this problem from distributing the eight to [(-1/6) - 1], the seven to -1/6, and the negative five to -1/6.
(-8/6) - 1 + 3 = (-7/6) - 6 + 5/6
NOTE: The parenthesis are not necessary at this point. It is just used to organize the terms. Your math teacher will explain this to you in the future.
At this point, it is as easy as just simplifying the problem.
-8/6 + 2 = -2/6 - 6
Now, you can go two ways to solving this equation. You can either make every whole number turn into the same denomator as the other fractions, or you can multiply each side with the same number as the denomator in each fraction. I usually just multiply each side with the denomator.
6(-8/6 + 2) = 6(-2/6 - 6)
-8 + 12 = -2 - 36
4 = -38
What? That's not possible, how can four equal negative thirty eight?!? Well, this is one of the main reasons why we check our answers. (Unless your teacher told you to not check your answer).
8(x - 1) + 3 = 7x - 6 - 5x
Okay, the first thing you should do is distribute the eight to x-1. The right side does not need distribution.
8x - 8 + 3 = 7x - 6 - 5x
Now, the next thing you should do is combine the like terms, and the terms that are different, you seperate them into different sides of the equation. So, for the terms that contain x, I usually put them on the left side of the equation, and for the terms that are normal numbers, I just put them on the right side of the equation. So combine the like terms.
8x - 5 = 2x - 6
You simply just add negative eight to three and 7x to negative 5x. Now, after you have done this, it is time to seperate the different terms to different sides of the equation. In this case, we must subtract both sides of the equation by 2x so that the x terms will remain on the left, and we must add five to both sides so that the number terms will stay on the right. Watch closely.
8x - 2x - 5 = 2x - 2x - 6
6x - 5 = -6
6x - 5 + 5 = -6 + 5
6x = -1
After you have done this, it is time to divide each side so that the x terms will remain as one x. So in this case, we divide both sides by six.
6x/6 = -1/6
x = -1/6
x = -1/6 is your final answer, but we're not done yet. Sometimes in an equation you might want to check that the resultant of the variable, x, when plugged in to the equation, fits perfectly, and checking the equation will make sure your resultant is correct. So, for the equation 8(x - 1) + 3 = 7x - 6 - 5x, we just plug in -1/6 to every x in that equation. Watch closely.
8[(-1/6) - 1] + 3 = 7(-1/6) - 6 - 5(-1/6)
At this point, just use the PEMDAS rule to find that -1/6 is truly x. So like before, you start this problem from distributing the eight to [(-1/6) - 1], the seven to -1/6, and the negative five to -1/6.
(-8/6) - 1 + 3 = (-7/6) - 6 + 5/6
NOTE: The parenthesis are not necessary at this point. It is just used to organize the terms. Your math teacher will explain this to you in the future.
At this point, it is as easy as just simplifying the problem.
-8/6 + 2 = -2/6 - 6
Now, you can go two ways to solving this equation. You can either make every whole number turn into the same denomator as the other fractions, or you can multiply each side with the same number as the denomator in each fraction. I usually just multiply each side with the denomator.
6(-8/6 + 2) = 6(-2/6 - 6)
-8 + 12 = -2 - 36
4 = -38
What? That's not possible, how can four equal negative thirty eight?!? Well, this is one of the main reasons why we check our answers. (Unless your teacher told you to not check your answer).
