Algebra 1 Help?

Question

Solving Equations with Variables on Both Sides

x + 2 = x = 4

I need help on how to do it. I don't want the answer. I want steps on how to figure it out. I really don't get it and please be very precise.

I also need help on these kinds

-2x + 8 = 2x + 4

2(f + 3) + 4f = 6 + 6f

I really don't get it. Even if you do tell me the answers these questions are Reteach questions. I don't turn these in for any credit.

Answer 1

x + 2=x = 4? How can x equal both 4 and 2? Honestly I'm not quite sure how to do that.

On the second kind you just get the variables by itself.

-2x + 8 - 8 = 2x + 4 - 8
-2x = 2x - 4
-2x - 2x = 2x - 2x - 4
-4x = -4
4x = 4
x = 1

Hope this helps! Remember, you can do any operation to one side, as long as you do the same thing to the other.

Answer 2

Hello,
The first one is weird.

In general we must isolate the variable by putting it on one side by itself.

So we need to decide which side on which to put it (it doesn't matter which one you choose).

In the second one -2x + 8 = 2x + 4 lets put x on the left by itself. To do this we have to to move remove the 8 from the left by doing the opposite of the operation so instead of adding 8 we subtract 8 and to keep the equation in balance we have to so it to both sides so it looks like this
-2x + 8 - 8 = 2x + 4 - 8 giving us -2x = 2x -4 now we have to remove the 2x from the right side by doing the opposite so we subtract 2x from both sides and we have -2x -2x = 2x -4 -2x which is -4x = -4 now to isolate x we need to remove the -4 in from of it to the other side so instead of multiplying by -4 we need to divide both sides my -4: (-4x)/-4 = -4/-4 so s0 x = 1.

For the third one first remove the parenthesis. Giving us
2f + 2*3 + 4f = 6 + 6f and we have 2f +6 + 4f = 6 + 6f combine the f giving us 6f + 6 = 6 + 6f. When this is finished by using the same method as above you get 0 = 0. This is a true statement s that means that any real number that you put in will make the equation true. So the solution is All Reals.

Hope this helps!!

Answer 3

Do you mean this equation:
x + 2 = x + 4

If so, combine like or similar terms by transposition (transfer of a term from one side of an equation to another and the reversal of its sign)

To illustrate, let me do the other problems :
-2x + 8 = 2x + 4

Transpose -2x to the other side of the equation :
8 = 2x + 2x + 4
Note, that the sign was reversed.
8 = 4x + 4
Transpose 4 to the other side of the equation (likewise, the sign is reversed)
8 - 4 = 4x
4 = 4x
To solve for x, divide both sides of the equation by 4
1 = x


2(f + 3) + 4f = 6 + 6f
In this problem, you have to perform multiplication first, by distributive property of multiplication:
2f + 6 + 4f = 6 + 6f
Combine similar terms. You can already transpose at the same time:
2f + 4f - 6f = 6 - 6
0 = 0

Answer 4

x + 2 = x + 4

What you need to do is get the variables on one side, and the numbers on the other. So...

x + 2 = x + 4
Subtract two from both sides to get x = x + 6
Subtract x from both sides to try to isolate the variable to get 0 = 6

Well, that one you either typed in wrong or doesn't have a solution. Because zero does not equal six.

-2x + 8 = 2x + 4
Add 2x to both sides to get 8 = 4x + 4
Subtract four from both sides to get 4 = 4x
Divide both sides by four to get x = 1

2(f + 3) = 4f = 6 + 6f
Distribute the 2 to get 2f + 6 + 4f = 6 + 6f
Combine the Fs to get 6f + 6 = 6f + 6
Subtract six from both sides to get 6f = 6f
Divide both sides by six to get f = f
F can be anything- it has an infinite number of solutions.

Hope I helped!

Answer 5

What you need to do is move the variables to one side of the = and the numbers to the other. for
x+2 = x+4, add -1x to both sides and add -2 to both sides. You get 0 = 2. This is impossible so there are no answers.

On the next, add 2x to both sides and add -4 to both sides. This time there will be an answer.

The third, do out the 2(f + 3) which is 2f + 6 Then add the 4f in, getting 6f + 6. This is the same as what is on the other side so that means it's always true no matter what f is.

Answer 6

a)
This is not possible.... x+2=x=4
x+2 cannot also equal x

b)-2x+8=2x+4
Step 1: Bring common elements on the same sides (all x's on one side and all non-variables on other side)
Like this: -2x-(2x)+8-(8) = 2x-(2x)+4-(8)
thus -4x=-4
Step 2: Divide the coefficient on the variable (-4) off both sides....-4x/-4=-4/-4
and thus x=1

c) 2(f+3)+4f=6+6f
Step 1: Expand: 2(f)+2(3)+4f=6+6f
thus 2f+4f+6=6+6f
thus 6f+6=6+6f
Step 2: Bring all common elements on same sides
6f-6f+6-6=6-6+6f-6f
thus gives 0=0 thus these two equations are exactly the same.

Answer 7

not quite sure about that one.
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