Key Points

An equation is a statement of equality between two algebraic expressions. It always contains an equal sign (=), which separates the Left Hand Side (LHS) from the Right Hand Side (RHS).

Solving an equation means finding the value of the unknown variable that makes the LHS equal to the RHS. This specific value is called the solution of the equation.

An equation is like a balanced weighing scale. Performing the same operation (addition, subtraction, multiplication, or division) on both sides of the equation maintains the equality.

The goal is to isolate the unknown variable on one side of the equation. This is done by applying inverse operations systematically to both the LHS and RHS.

To solve an equation, use the inverse operation to undo operations on the variable. Addition undoes subtraction, and multiplication undoes division.

To remove a number that is added to the variable, subtract that number from both sides. To remove a number that is subtracted, add that number to both sides.

To remove a number that is multiplying the variable, divide both sides by that number. To remove a number that is dividing the variable, multiply both sides by that number.

For equations like 2x + 5 = 15, first undo the addition or subtraction (subtract 5 from both sides), and then undo the multiplication or division (divide by 2).

If an equation has variables on both sides, like 5x + 2 = 3x + 10, first collect all the variable terms on one side and all the constant terms on the other side.

To solve a word problem, first identify the unknown quantity and represent it with a letter (variable). Then, translate the given information into a mathematical equation and solve it.

After finding a solution, you should substitute the value back into the original equation. If the LHS equals the RHS, your solution is correct.

Transposition is a shortcut where a term is moved from one side of the equation to the other. When a term is moved, its sign changes: addition becomes subtraction, and multiplication becomes division.

The field of algebra, known as 'Bijaganita' in ancient India, was systematically developed by mathematicians like Brahmagupta in works like 'Brahmasphutasiddhanta' (628 CE).