## Hard Algebraic Equations

#### Solving equations

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**

2(x + 5) = 18

:- 2 => 2(x + 5) :- 2 = 18 :- 2

x + 5 = 9

- 5 => x + 5 - 5 = 9 - 5

x = 4

**E.g.2**

5(x - 2) = 2(x - 3)

5x - 10 = 2x - 6

+10 => 5x - 10 + 10 = 2x - 6 + 10

5x = 2x + 4

-2x => 5x - 2x = 2x - 2x + 4

3x = 4

:-3 => 3x / 3 = 4 /3

x = 1.3

**E.g.3**

4(x + 4) + 3(x -3) = 2(x -3) + 12

4x + 16 + 3x - 9 = 2x - 6 + 12

7x + 7 = 2x + 6

- 7 => 7x + 7 - 7 = 2x + 6 - 7

7x = 2x - 1

-2x => 7x - 2x = 2x - 2x -1

5x = -1

:-5 => 5x / 5 = -1 / 5

x = -0.2

**E.g.4**

(x + 5) / 4 = (x -3) / 2

X 4 => 4 X (x + 5) /4 = 4 X (x- 3) / 2

(x + 5) = 2 (x -3)

x + 5 = 2x - 6

- 5 => x +5 -5 = 2x - 6 - 5

x = 2x - 11

-2x => x - 2x = 2x - 2x -11

-x = -11

-1 X x = 11

**E.g.5**

3 + 2(x + 5) = 3 - (2x - 1)

3 + 2x + 10 = 3 -2x + 1

13 + 2x = 4 - 2x

-13 => 2x + 13 - 13 = 4 - 2x - 13

2x = -2x - 9

+2x => 2x + 2x = 2x - 2x - 9

4x = -9

:- 4 => 4x / 4 = -9 / 4

x = -2.25

**Practice is the key to mastering maths; please visit this page, for more worksheets.**

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

- 2(x + 9) + 3 = 13
- 3(x + 9) - 6 = 19
- 3(x - 2) = 2(x - 4) + 7
- 5(x - 3) + 2(x + 1) = 2(x - 2)
- 4(x - 2) - 2(x - 1) = 3x + 16
- 2x + 4(2x - 1) = 4(x + 2)
- 3(x + 3) - 2(x + 1) = 2(x -1) + 4x
- 2 - 3(x + 1) = 2(2x -3)
- 4(x -3) - 3(x + 2) = 5 + 2(x + 2)
- 3 - (x-3) = 4 + (x - 2)