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**

I think of a number, add 7 and the answer is 10. Find the number.

Let the number be x.

x + 7 = 10

-7 => x + 7 -7 = 10 -7

x = 3

The number is 3.

**E.g.2**

I think of a number, take away 5 and the answer is 10. Find the number.

Let the number be x.
x - 5 = 10

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

x = 15

The number is 15.

**E.g.3**

I think of a number, multiply by 3 and the answer is 30. Find the number.

Let the number be x.

3x = 30

:- 3 => 3x / 3= 30 /3

x = 10

The number is 10.

**E.g.4**

I think of a number, multiply it by 2, take away 4. The answer is 10. Find the number.

Let the number be x.
2x - 4 = 10

+ 4 => 2x - 4 + 4 = 10 + 4

2x = 14

:- 2 => 2x / 2 = 14 / 2

x = 7

The number is 7.

**E.g.5**

I think of a number, divide by three, add 7. The answer is 10. Find the number.

Let the number be x.
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

The number is 9.

**E.g.6**

I think of a number, take away three and then divide by 4. The answer is 3. Find the number.

Let the number be x.

(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

The number is 15.

**E.g.7**

I think of a number, multiply by 3, add 3. The answer is the same, if I add 10 to the number. Find the number.

Let the number be x.

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

The number is 3.5.

**E.g.8**

I think of a number, multiply by 2, take away 4. The answer is the same if I multiply it by 5 and then add 8. Find the number.

Let the number be x.

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

The number is -4.

**E.g.9**

The width of a rectangle is 2cm less than the length. The perimeter is 20 cm. Find the length and the area.

let the width be x. So, the length = x + 2.

x + x + 2 + x + x + 2 = 20

4x + 4 = 18

-4 => 4x + 4 - 4 = 20 - 4

4x = 16

:-4 => 4x / 4 = 16 / 4

x = 4

Width = 4cm; length = 6cm;

Area = 24 cm^{2}.

**E.g.10**

The sum of two consecutive odd numbers is 52. Find the numbers.

Let the first number be x. Then the next one is x + 2.

x + x + 2 = 52

2x + 2 = 52

-2 => 2x + 2 - 2 = 52 - 2

2x = 50

:-2 => 2x / 2 = 50 / 2

x = 25

The numbers are 25 and 27.

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

- I think of a number, multiply by 4 and add 5. The answer is 29. Find the number.
- I think of a number, add 3 and the result is multiplied by 4. The answer is 28. Find the number.
- I think of a number, add 6 and divide by 3. The answer is 5. Find the number.
- I think of a number, multiply by 4, and add 6. The result is then multiplied by 5 and the answer is 70. Find the number.
- Twice a number added to 5 is the same as the number added to 10. Find the number.
- A number multiplied by 5, add 4 is the same as 6 times the number. Find the number.
- Three times a number, add nine, divided by 6 is the same as the number itself. Find the number.
- Twice a number added to 6 is the same as ten subtracted from six times the number. Find the number.
- The sum of three consecutive numbers is 78. Find the numbers.
- The sum of three consecutive even numbers is 44. Find the numbers.

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