Simple Algebraic Equations

seesaw

 

An equation is almost a sort of seesaw: you add something to the left, lose the balance and are forced to do the same to the right; you divide and multiply by something, once again, the same must be done to the other side; if you subtract something, there is no exception. Therefore, solving equation means, getting rid of everything around x by seesaw method.


E.g.1

x + 5 = 8
- 5 => x + 5 -5 = 8 - 5
x = 3


E.g.2

x - 5 = 10
+ 5 => x -5 + 5 = 10 + 5
x = 15


E.g.3

2x = 10
:- 2 => 2x / 2 = 10 /2
x = 5


E.g.4

x / 5 = 2
X 5 => x /5 X 5 = 2 X 5
x = 10


E.g.5

2x - 4 = 10
+ 4 => 2x - 4 + 4 = 10 + 4
2x = 14
:- 2 => 2x / 2 = 14 / 2
x = 7


E.g.6

2x + 4 = 10
- 4 => 2x + 4 - 4 = 10 - 4
2x = 6
:- 2 => 2x / 2 = 6 / 2
x = 3


E.g.7

x/3 + 7 = 10
-7 => x/3 + 7 - 7 = 10 - 7
x/3 = 3
X 3 => x/3 X 3 = 3 X 3
x = 9


E.g.8

(x - 3) / 4 = 3
X 4 => (x-3) /4 X 4 = 3 X 4
(x-3) = 12
+ 3 => x - 3 + 3 = 12 + 3
x = 15


E.g.9

3x + 3 = x + 10
-3 => 3x + 3 -3 =x + 10 - 3
3x = x + 7
- x => 3x - x = x - x + 7
2x = 7
:-2 => 2x / 2 = 7 / 2
x = 3.5


E.g.10

2x - 4 = 5x + 8
+4 => 2x - 4 + 4 = 5x + 8 + 4
2x = 5x + 12
-5x => 2x - 5x = 5x - 5x + 12
-3x = 12
:--3 => -3x/-3 = 12 / -3
x = -4

Now, in order to complement what you have just learnt, work out the following questions:


  1. x + 9 = 13
  2. 2x + 9 = 19
  3. 3x - 9 = 18
  4. 5x + 9 = 2x + 21
  5. 8x - 9 = 3x + 16
  6. 2x + 9 = 4x + 17
  7. 3x + 19 = x + 9
  8. 2x + 9 + 3x = 34
  9. 4x + 9 + 3x = 5x + 13
  10. 5x + 9 + 2x = 3x + 13 - x


 

 

Recommended Reading

 

Maths is challenging; so is finding the right book. K A Stroud, in this book, cleverly managed to make all the major topics crystal clear with plenty of examples; popularity of the book speak for itself - 7th edition in print.

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