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They are:-

If any number is added or subtracted from both sides of an equation, the resulting equation has the same solution as the original.

If each side of equation is multiplied or divided by non-zero number, the resulting equation has the same solution as the original.

This can be easily understood by taking the separate examples for using the rules

Use Addition – Subtraction Rule

To eliminate – 15, add 15 on both sides

x – 15 + 15 + 7= 25 + 15

x + 7= 40

To eliminate + 7, subtract 7 on both sides

x + 7 – 7 = 40 – 7

x = 33

Hence the required solution

This problem helps to understand the Addition – Subtraction rule

Use Multiplication and Division rule.

Multiply by 3 on both sides, 3 in the denominator gets cancelled

3 X 2x/3 = 8 X 3

2x = 24

Divide by 2 on both sides

X= 12; Solution obtained

These examples we applied basic rules for solving linear equation with one variable.