Multi-step equations?

Question

I really suck at algebra! I need some help!

this were some problems of my homework

I need to solve this multi step equations

I know they are very basic, but I don't know how to do all the procedure

1) 2x+4

_______= 5

6

2) 3x-2

__________= x

2

3) 4(3-y)+y = 22+2y

4) 4v-5(3v+10) = 126

can someone explain me?

Answer 1

1)  (2x+4) / 6 = 5

multiply by 6

2x+4 = 30

2x = 30 - 4

2x = 26

x = 13

2) (3x-2) / 2 = x

multiply by 2

3x - 2 = 2x

x = 2

3) 4(3-y)+y = 22+2y

12 - 4y = 22 + 2y

6y = 12 - 22

6y = - 10

y = - 5/3

4) 4v - 5(3v +10) = 126

4v - 15v +50 = 126

- 11v = 126 - 50

11v = - 76

v = - 76/11

.

Answer 2

cross multiply

(2x +4)(1) = 6*5

2x +4 = 30

2x = 26

x=13

3x -2 = 2x

x=2

12 - 4y +y = 22 +2y

12 -3y = 22 + 2y

-10 = 5y

-2 =y

Answer 3

well i'm not sure about 1 and 2 but 3 and 4 i think i might know what to do there it's just cross multiplication like so

4(3-y)+y=22+2y

multiply 4 with 3 and -y so ur answer for the first step is going to be

12-4y+y=22+2y  then add -4y with y like so

12-3y=22+2y then add -3y to both sides like so

12-3y=22+2y

'''  +3y   '''  +3y

so ur next answer is going to be

12=22+5y

-22 -22

then u add 22 to both side because u want Y to be alone

when u add to both sides the positive or negative sign changes

so u get

-10=5y then u divide 5 to both sides and u get ur answer like so

___

5y

and u get

-2=y

number 4 looks weird to me for some reason there might be a remainder so think the answer is going to be a fraction maybe but it looks weird to me but try to do the same thing as i did for number 3

Answer 4

1.            2x+4 = 30

               2x = 26

                x=13

2.   3x-2 = 2x

       x-2=0

         x=2

3. 12 - 4y + y = 22 +2y

    12 -3y = 22 + 2y

     -10 = 5y

         -2 = y

4. Apply the concepts I used to figure this one out on your own.

Answer 5

1)

2x+4

_______= 5

6

Step 1 -First of all, we want to get rid of the fraction bar. To do this we have to make it a whole number. Since fractions are a form of division, we have to do the inverse (opposite) operation, which happens to be multiplication. So, we multiply both sides of the equation by 6, because  2x + 4 / 6   x    6 will cancel out the 6 at the bottom, leaving you with 2x + 4 = 5. (This works with all numbers.) We have to remember that whatever we do to one side, we have to do to the other, otherwise we'd be messing up the equation. Since we multiplied the left by 6, we multiply the right by 6. 5 x 6 = 30, so we know have 2x + 4 = 30.

Step 2: Now we have to get x by itself. First we get rid of the normal numbers,. By 'normal', I mean anything that isn't attached to x. The only  'normal' one is 4, so we have to get rid of it first. Since 4 is being added in this equation, we have to use subtraction, becase it is the inverse operation of addition. When we subtract on the left, we're left with 2x. When we subtact on the right we get 26. (30 - 4 = 26) Now we have 2x = 26.

Step 3: Last step. Since 2x is the same as 2 times x, we know that this is multiplication. The inverse operation is division, so we just divide both sides by 2. 2x / 2 is x, and 26 / 2 is 13.

So your final answer is x = 13.

2)

3x-2

__________= x

2

I won't walk you through it since you should alread know what to do, but I will show the steps.

3x - 2 = x times 2 ( 3x - 2 = 2x)

We want the all the like terms on the same side. This means get all the numbers with an 'x' on the same side and all the numbers without one on the other.

The simplest way to do this is to subtract 3x from both sides. This will get the -2 by iteslf and at the same time but the 'attatched' numbers together.

-2 = 2x - 3x (-2 = -x)

Since we have the answer of -x, (it's -2 if you didn't already know), we know that x = the opposite of -2. (Negative and positive numbers are always opposites.) Which means that x = 2.



3) 4(3-y)+y = 22+2y

Step 1: Since there is multiplication involved, 4(3-y), multiply it out. 4 x 3 = 12 and 4 times y  is 4y, so you get 12 - 4y.

Step 2: Now that you have 12 - 4y + y = 22 + 2y, we can dd like terms. -4y + y is -3y. Now you have 12 - 3y = 22 + 2y. We know have to add one of the y's to the other. I recommend adding 3y to both sides because + is always easier than -. Now you should have 12 = 22 + 5y.  Now just subtract 22 to get the normals on one side.12 - 22 = -10, so you're left with

-10 = 5y.

Step 3: Divide by 5 to get y by iteslf. y = -2

4) 4v-5(3v+10) = 126

Same old same old.

Distribute. -5(3v+10) = -15v + 50

Add like terms. 4v - 15v = -11v.

Get normals together. -50 on both sides (126 - 50 = 76)

Divide. -11v/11 = 76/11 = v=76/11, or 6 10/11