The Easiest Way to Understand Algebra Equations by Skudaev Sergey

Author:Skudaev, Sergey [Skudaev, Sergey]
Language: eng
Format: epub
Tags: Algebra
Published: 2015-01-08T22:00:00+00:00

b + c = X

X = b + c

APPENDIX 2.

PRACTICE 4. SOLUTIONS.

1. bX - 2b = aX - 2a

Add 2ab to both sides of the equation :

bX - 2b + 2b = aX - 2a + 2b

bX = aX - 2a + 2b

Subtract aX from both sides of the equation :

bX - aX = aX - 2a + 2b - aX

bX - aX = 2b - 2a

Factor X out of term: bX - aX

X(b-a) = 2(b - a)

Divide both sides of the equation by (b - a):

X(b-a)/(b - a) = 2(b - a)/(b - a)

Where (b-a) is not equal 0!

X = 2(b-a)/(b-a) = 2

2. b - 2bX = a - 2aX

Subtract b from both sides of the equation :

b - b - 2bX = a - b - 2aX

-2bX = a - b - 2aX

Add 2aX to both sides of the equation :

-2bX + 2aX = a - b - 2aX + 2aX

-2bX + 2aX = a - b

2aX - 2bX = a - b

2X(a - b) = (a - b)

Divide both sides of the equation by (a - b):

2X(a - b)/(a - b) = (a - b)/(a - b)

2X = 1

Divide both sides of the equation by 2:

2X/2 = 1/2

X = 0.5

3. aX - bX = 1

Factor X out of term: aX - bX

X(a - b) = 1

Divide both sides of the equation by (a - b):

X(a - b)/(a - b) = 1/(a - b)

X = 1/(a - b)

4. aX - bX - cX = 2a - 2b - 2c

X(a - b - c) = 2(a - b - c)

Divide both sides of the equation by (a - b - c):

X(a - b - c)/(a - b - c)=2(a - b - c)/(a - b - c)

X = 2

5. 3abX - 5a = 3acX + 13a

Add 5a to both sides of the equation :

3abX - 5a + 5a = 3acX + 13a + 5a

3abX = 3acX + 18a

Subtract 3acX from both sides of the equation :

3abX -3acX = 3acX + 18a -3acX

3abX - 3acX = 18a

Factor 3aX out of term: 3abX - 3acX

3aX(b - c) = 18a

Divide both sides of the equation by (b - c):

3aX(b - c)/(b - c) = 18a/(b - c)

Divide both sides of the equation by 3a:

3aX/3a = 18a/3a (b - c)

X = 6/(b - c)

6. aX - bX = ac - bc

Factor X out of term: aX - bX

X(a - b) = c(a - b)

Divide both sides of the equation by (a - b):

X(a - b)/(a - b) = c(a - b)/(a - b)

X = c

7. 9a - 4X = 5a - 2X

Add 4X to both sides of the equation :

9a - 4X + 4X = 5a - 2X + 4X

9a = 5a - 2X + 4X

9a = 5a + 2X

Subtract 5a from both sides of the equation :

9a - 5a = 5a + 2X - 5a

4a = 2X

2X = 4a

Divide both sides of the equation by 2:

2X/2 = 4a/2

X = 2a

8. X - aX = 2 - 2a

Factor X out of term: X

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