Please explain this so that a dummy could understand.....?

Question

I do not understand this. I have asked for help from the teacher and she (and our text books) talk as if we already know how to do these problems. I follow the exampes in the book and they answers to do come out right. Can you explain step by step? PLEASE.

3/4x-5 = 2/3x+1/4

1/2b - 19/6 = 1/3b+5/6

a+1/3 + a-1/5 = 2/15

3+p/3 - 4p=1 - p+7/2

Answer 1

Think of the equation as a balanced scale. The = sign is the balance

point, and the left side of the scale in in perfect balance with the right side.

You are permitted to mess around with the items on either side of the

scale, PROVIDED that whatever you do to one side of the scale, you

must do the same thing to the other side. NO EXCEPTIONS!!!

The tools you have to do the messing around with are

addition, subtraction, multiplication, and division.

Now let's go to work.

3/4x-5=2/3x+1/4

Our aim is to get the x terms on one side.

Add 5 to both sides

3/4x-5+5=2/3x+1/4+5

Tidy up.

3/4x=2/3x+5 1/4

Subtract 2/3x from both sides

3/4x-2/3x=2/3x-2/3x+5 1/4

Tidy up

3/4x-2/3x=5 1/4

I cannot add or subtract fractions unless the denominators are the same. So 3/4x-2/3x requires the same denominator.

The Common denominator is 12

Therefore 3/4x becomes 9/12x, and -2/3x becomes -8/12x

I'm in business.

9/12x-8/12x=5 1/4

1/12x=5 1/4

I don't like the looks of 5 1/4, so  I'll turn it into a proper fraction.

5 1/4 =20/4+1/4, or 21/4

Now I have 1/12x=21/4

Now, how to figure out what 1x is.

I'll multiply both sides of the equation by 12

12(1/12x)=21/4(12)

1x=63

We usually don't show the 1 in front of x, it being understood it's there.

So x=63, and I'm done.

And that's how you do these things.

Once you get the hang of it, you can speed things up a lot by doing

two steps at a time. I show you this in the next problem.

1/2b-19/6=1/3b+5/6

Subtract 1/3b and add 19/6 from both sides at the same time.

1/2b-1/3b-19/6+19/6=1/3b-1/3b+5/6+19/6

1/2b-1/3b=5/6+19/6

3/6b-2/6b=24/6

1/6b=4

b=24

Did you see all this? I found the common denominator for 1/2b and -1/3b in my head, (it is 6), then changed 1/2 to 3/6 and -1/3 to -2/6,

again in my head

Lastly, I multiplied 1/6b by 6 to get b, and obeying the rule that the

other side must be treated the same, I multiplied 4 by 6 as well.

I' m now going to do the last 2 without explanations.

a+1/3+a-1/5=2/15

a+a=2/15-1/3+1/5

2a=2/15-5/15+3/15

2a=0

a=0 (I divided both sides by 2: 2a/2 is a, 0/2 is 0)

3+p/3-4p=1-p+7/2

p/3-4p+p=1+7/2-3

p/3-3p=7/2-2

p/3-9p/3=7/2-4/2

-8p/3=3/2

Multiply both sides by 6

-16p=9

Multiply both sides by -1

16p= -9

p= -9/16

I wish you success.

Cheers

Answer 2

You need to understand:

A. To be able to solve, all the x's must be on one side of the equal sign and the numbers not associated with x's on the other side.

B. Whatever you do on one side of the = sign, you must also do on the other side, so that it is still equal. For instance, 5 + 3 = 7 + 1.

And then 5 + 3 - 2 = 7 + 1 - 2. Or (5 + 3) divided by 4 = (7 + 1) divided by 4. Do these so that you have confidence when you do it with symbols as well as numbers.

C. That you can write fractions like 2/3 as another fraction like 4/6 or 16/24.

3/4x-5 = 2/3x+1/4

Subtract 2/3x both sides:

3/4x-5 - 2/3x = 2/3x+1/4 - 2/3x

(3/4x - 2/3)x - 5 = 0+1/4......3/4-2/3 = 9/12 - 8/12 = 1/12, so

1/12x-5 = 1/4

Add 5 both sides:

1/12x-5+5 = 1/4+5

1/12x + 0 = 1/4 + 20/4

1/12x = 21/4

Now, because 1/12 times 12 = 1, you multiply both sides of the = by 12:

1x = (1/4)(12) = (21/4)(12) = 21(3) = 63

Your solution is: x = 63

Do this a few times and then try the rest, before looking at my solutions.

1/2b - 19/6= 1/3b + 5/6

1/2b - 1/3b - 19/6 + 19/6 = 1/3b - 1/3b + 5/6 + 19/6.....you can do this in one step: subtract 1/3b both sides and add 19/6 both sides

1/6b = 24/6

(1/6)6b = (24/6)(6)

b = 24

The rest should now be easy. Try them before peaking.

a+1/3+a-1/15 = 2/15

2a + 5/15 - 1/15 = 2/15

2a + 4/15 = 2/15

2a + 4/15 - 4/15 = 2/15 - 4/15

2a = -2/15

2a/2 = (-2/15)/2

a = -1/15

3+p/3-4p=1- p+7/2

p/3-4p+p=1-7/2-3

p/3 - 3p = -11/2....To get p/3 as just 1p, multiply both sides by 3

(p/3)3 -3p(3) = (-11/2)(3)

p - 9p = -33/2

-8p = -33/2

Divide both sides by -8:

p = (-33/2)/(-8) = 132

All the best.

Answer 3

The letter X is an unknown variable and the job is to solve the equation and find a value for X. To start we write down the equation

3/4x - 5 = 2/3x + 1/4 now move the number on the left side of the = sign to the right side of the equals sign remember its sign changes so -5 becomes +5

3/4x = 2/3x + 1/4 + 5 Then move the x number on the right over to the left side of the equals sign changing sign again 2/3x becomes -2/3x

3/4x - 2/3x = 1/4+5 resolve both sides 3/4x - 2/3x = 51/4

common denominator for fraction

9/12x - 8/12x = 1/12x

1/12X = 51/4 now move the fraction from left side over to right side changing sign again 1/12 becomes 12/1

so x = 12 times 51/4= 63

Repeat this process for all examples

1/2b - 19/6 = 1/3b + 5/6 move the numbers to right side

1/2b = 1/3b + 5/6 + 19/6 move the b's to the left side

1/2b - 1/3b = 5/6 + 19/6 resolve each side using fraction common denominator

3/6b - 2/6b = 24/6

1/6b = 4

b = 4 times 6/1

b = 24