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The Easiest Way to Understand Algebra. Algebra equations with answers and solutions. Sergey D. Skudaev
Читать онлайн.Название The Easiest Way to Understand Algebra. Algebra equations with answers and solutions
Год выпуска 0
isbn 9785449091154
Автор произведения Sergey D. Skudaev
Жанр Руководства
Издательство Издательские решения
– 2X = a – b
Let’s divide both sides of the equation by -2
To make your result more beautiful, you can multiply the numerator and the denominator by – 1.
The next equation:
3a – 6X = 6X – 9a
You can see that on the left side of the equation you have -6X
and on the right side +6X. It is more convenient for you to have a + in front of X, therefore, you leave +6X on the right side and get rid of -6X on the left side of the equation.
Add 6X to both sides of the equation:
3a – 6X +6X = 6X – 9a +6X then 3a = 12X – 9a
Add 9a to both sides of the equation:
3a +9a = 12X – 9a +9a then 12a = 12X
X = a
Do not read any more until you perform some exercises.
Practice 3. Solving the equations
Answers: page 20
Solutions: page 27
(Solve for X)
1. 1 – X = 5 – a
2. 1 – 2X = X – 4
3. a – 3X = b – X
4. 2a – 4X = 2X – 4a
5. 4b – 2X = 2X – 4b
6. ab + aX = 2aX + ac
7. ab + aX = 2aX – ac
Let us continue and discuss the equation: aX – bX = a – b
Factor out X which is a common factor for binomial aX – bX,
then you will get X (a – b) = a – b
Divide each part of the equation by a – b
X (a – b) / (a – b) = (a – b) / (a – b)
X = 1
Do not read any more until you perform some exercises.
Practice 4. Solving the equations
Answers: page 20
Solutions: page 30
(Solve for X)
1. bX – 2b = aX – 2a
2. b – 2bX = a – 2aX
3. aX – bX = 1
4. aX – bX – cX = 2a – 2b – 2c
5. 3abX – 5a = 3acX +13a
6. aX – bX = ac – bc
7. 9a – 4X = 5a – 2X
8. X – aX = 2 – 2a
9. aX – bX = b – a
Let us continue and solve the equation: aX – bX = 2b – 2a
Factor out X from the left side of the equation.
X (a – b) = 2b – 2a
Factor out 2 from the right side of the equation.
X (a – b) = 2 (b – a) then divide both sides by (a – b)
Factor out (-1) from the denominator
Or you can simplify this algebraic expression by factoring out (-1) from the numerator
Practice 5. Solving the equations
Answers: page 20
Solutions: page 32
Solve for X.
1. 5aX – 5bX = 10b – 10a
2. aX – bX – cX = c + b – a
3. 2X – 3aX = 6a – 4
4. 3aX – 9bX = 27b – 9a
5. 4bX – cX = 8c – 32b
6. abX – acX = ac – ab
7. X/2 – aX = 1 – 2a
8. aX/5 +2a = 5a – 4aX
You can find answers in appendix 1 and solutions in appendix 2.
2. SYSTEM OF EQUATIONS
Look at the equation X + Y = 3. X and Y are unknown. You cańt find neither X nor Y from this equation. You need additional information about the “relationship” between them. Such information may be included in an additional equation. For example: X – Y = – 1. Now you have a system of 2 equations:
1. X + Y = 3
X – Y = -1
There are several ways to solve it. The first way: solve for X in any equation, for example, the first one.
In order to do that, subtract Y from each side of the equation:
X + Y – Y = 3 – Y; Find X
X = 3 – Y
Then put (3 – Y) in place of X in the second equation (X – Y = -1).
You will obtain: 3 – Y – Y = -1 or 3 – 2Y = -1
Now solve that equation for Y. Add 2Y to
3 – 2Y +2Y = -1 +2Y
3 = -1 +2Y
Add 1 to the both sides of the equation.
3 +1 = -1 +1 +2Y
4 = 2Y
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