The Easiest Way to Understand Algebra. Algebra equations with answers and solutions. Sergey D. Skudaev
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Название: The Easiest Way to Understand Algebra. Algebra equations with answers and solutions
Автор: Sergey D. Skudaev
Издательство: Издательские решения
Жанр: Руководства
isbn: 9785449091154
isbn:
2X = 2bc +4b. Then
2X / 2 = 2bc / 2 +4b / 2
Then X = bc +2b
You can factor out b and get
X = b (c +2)
Whenever you don’t know the rule, you can put any numbers in place of the letters and check equality. Discover rules by yourself.
Let us solve a more complicated equation:
Multiply both sides of the equation by 5X.
5X – 5 = 50X
Use the 2nd rule, subtract 5X from both sides:
5X – 5 – 5X = 50X – 5X
– 5 = 45X
or 45X = – 5
Divide both sides by 45
45X/45 = -5/45
X = – 1/9
The next equation:
Find the common denominator:
Since + aX – aX = 0, our equation becomes simple:
Use the 3rd rule: multiply both sides of the equation by (a + b)
Then b – bX = c (a + b)
Apply the 2nd rule, subtract b from both sides of the equation:
b – bX – b =c (a + b) – b
Then -bX =c (a + b) -b Divide both sides by b:
To make this algebraic expression more beautiful, multiply the numerator and denominator by (-1).
You can do that because (-1) / (-1) = 1. If you multiply any number by 1 the number will not be changed.
Then
The next equation:
– 2X = a – b
It is not convenient for you to have a minus in front of 2X.
You can change the equation into a more convenient form.
Let’s multiply both sides of the equation by -1
(-2X) (-1) = (a – b) (-1) then you get
2X = -a + b or 2X = b – a
Divide both sides by 2:
There is another way to solve this equation:
– 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. СКАЧАТЬ