# Equations in One Variable

## Example

Solve the following equation.

2x + 2 = 8

2x + 2 = 8

∴ 2x + 2 - 2 = 8 - 2

∴ 2x = 6

∴ x = 3

## Example

Solve the following equation.

3x - 5 = x - 17

3x - 5 = x - 17

3x - 5 + 5 - x = x - 17 + 5 - x

∴ 2x = - 12

∴ x = - 6

## Example

The length of a rectangle is 1 cm more than twice its breadth. If the perimeter of the rectangle is 50 cm, find its length.

Let the breadth of the rectangle be x cm.
Then the length of the rectangle will be (2x +1)cm.
2 × length + 2 × breadth = perimeter of rectangle

2 (2x + 1) + 2x = 50

∴ 4x + 2 + 2x = 50

∴ 6x + 2 = 50

∴ 6x = 50 - 2 = 48

∴ x = 8

Breadth of rectangle is 8 cm.

Length of the rectangle = 2x + 1 = 2 × 8 + 1

∴ Length of rectangle = 17 cm.

## Example

Solve the following equation.

The sum of two consecutive natural numbers is 69. Find the numbers.

Let one natural number be x.
The next natural number is x + 1
(x) + (x + 1) = 69
∴ x + x + 1 = 69
∴ 2x + 1 = 69
2x = 69 - 1
∴ 2x = 68
∴ x = 34

1st natural number = 34
2nd natural number = 34 + 1 = 35.

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