Can someone please help me with my math problems.?

Question

I am very confused on this why dont you do these problems the same way?

3a-6=a+4
3a-6+6=a+4+6
3a=a+10
3a-a=a+10-a
2a=10
2 2
a=5
7x-14=9x-6
7x-14-9x=9x-6-9x
-2x-14=-6
-2x-14+14=-6+14
-2x=8
-2 -2
x=-4
ok, notice how you add first in the first example and then subtract. Now notice how you subtract first and then add in the second example.
Now if I follow the way they did it in the second example for this problem
2x+7=6x-1
I get the wrong answer
2x+7=6x-1
8x+7=-1
-7 -7
8x=-8

Now if I use the second example I get
2x+7=6x-1
-4x+7=-1
+7 +7
-4x 6
Notice again I get the wrong answer. So can someone please explain to me how do you decide when to add and when to subtract or can someone tell me where I go wrong tih these problems because they are honestly making no sense to me at all.

Answer 1

It's not so much a matter of adding or subtracting uniformly. In all cases, you are adding the *additive inverse* of something to both sides of the equation. If that something is positive, then the additive inverse is negative, so you are essentially subtracting. Otherwise, you are adding.

For the problem 2x+7 = 6x-1, you add -6x to both sides, because that is the additive inverse of 6x. In other words, you are subtracting 6x.

You get -4x+7=-1, like you did before.

Now, you add -7 to both sides, because that is the additive inverse of 7. In other words, you are subtracting 7.

You get -4x = -8, so x=2.

Answer 2

the idea is to get the variable on one side and the numbers on the other. for 2x + 7 = 6x - 1, you want to move the 6x over to the 2x. since the 6x is positive, you subtract it from each side. 2x-6x+7=6x-6x-1, so -4x+7=-1. then subtract the 7. -4x+7-7=-1-7, so -4x=-8. divide the -4 and you get x=2 for the answer.

notice how the subtraction totally cancels out the number on one side ((6x-6x)-1 = 0-1 = 1). this is the idea behind it. to cancel something out, you'll need the opposite operation. if the 6x is positive, subtract a 6x (in other words, add a negative 6x). when the 4 is mulitplied by x, divide by four on both sides. think of what will get rid of the number you need to move, and do exactly that to both sides.

also, it doesn't matter what order you go in to move the numbers or to what sides you move the variables. if you'd moved the 2x to the right side, for example, you'd have gotten 7 = 6x - 2x - 1, or 7 = 4x-1, then 8=4x, then x=2. it works out the same.

Answer 3

The whole idea is getting all "x" elements onto one side, and getting the rest onto the other side. It does not matter if you do additions or subtractions first.
.
2x + 7 = 6x - 1
(Let's subtract first now, as you say)
2x + 7 - 6x = 6x - 1 - 6x (remember in the given example you omiited to take out 6x on both sides)
-4x + 7 = - 1
Now: -4x + 7 - 7 = - 1 - 7
-4x = - 8
Now divide both sides by (-4) so as to find x:
x = (-8)/(-4) = 2

Answer 4

2x + 7 = 6x - 1
-2x -2x
7 = 4x - 1
+1 +1
8 = 4x
/4 /4
2 = x

The first time you tried, you ADDED 6x to both sides, which would make 8x on the left and 12x on the right. You should have subtracted.

The second time you tried, you ADDED 7 to both sides, which would make 14 on the left and 6 on the right. You should have subtracted.

Do you see the pattern? You have to do whatever is necessary to get the variables on one side to be zero and the numbers on the other side to be zero. Subtract or add; whatever is necessary to get those zeroes.

Answer 5

I can shed some light on how to solve these equations. In both examples you have like variables on both sides of the equation. In the first example, you added 6 to both sides of the equation. That gave you the constant on the left, so you had to subtract a from both sides to get the variable on the right.

The second equation is similar in that it, too, has lioke variables on both sides. In this example, they decided to subtract 9x from both sides. I would have subtracted 7x from both sides, instead. It doesn't matter what you do to the equation, as long as you do the same thing to both sides. When there are variables on both sides of an equation, look to get rid if the one with the smaller coefficient. That way you will always be dividing by a positive number. It doesn't matter if the variable is on the right, or the left. It doesn't matter if you decide to add to both sides, or subtract. You just always do the opposite of what was done. Let me know if this helps. Good luck!

Answer 6

You need to do the same thing on both sides of the equal sign.
In your example, to solve the problem, you need to get 6x off from the right side of the equation, so you need to subract 6x from both sides.
2x+7=6x-1
2x+7-6x=6x-1-6x
Then to get the +7 off from the left side of the equation, you need to subract 7 from both sides
-4x+7=-1
-4x+7-7=-1-7
-4x=-8
Then to solve for x, you need to divide both sides by -4
-4x/(-4)=-8/(-4)
x=2

Answer 7

You are doing it wrong. This is the right answer.
2x+7=6x-1
2x+7-6x=6x-1-6x
-4x+7=-1
-4x+7-7=-1-7
-4x=-8
x=2

Answer 8

You are making it too confusing. If you need to remove a term from one side, look at whether it is being added, subtracted, multiplied, or divided.. Then, put it on the opposite side of the equation using the opposite operation.

Opposites
Adding ----- subtracting
Multiplying ---- dividing.

Answer 9

7x-14=9x-6
-7x -7x
-14=2x-6
+6 +6
-8=2x
divide by 2
x=-4

Answer 10

sorry dude i can't help you i am barley in the 6th grade