Key Points

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

An expression is a combination of numbers, variables, and operations, like 5x + 3. An equation states that two expressions are equal, for example 5x + 3 = 18.

An expression is considered linear if the highest power of the variable appearing in it is 1. For example, 2x + 1 is a linear expression, but x squared + 1 is not.

This is an equation which contains only one variable and is formed using linear expressions. The general form is ax + b = c, where a, b, and c are numbers and a is not zero.

The solution of an equation is the value of the variable that makes the equation a true statement. This means the value of the LHS becomes equal to the value of the RHS.

An equation is like a balanced scale. To keep it balanced, any mathematical operation (addition, subtraction, multiplication, division) you perform on one side must also be performed on the other side.

To solve such equations, the first step is to collect all terms with the variable on one side of the equation and all the constant terms on the other side.

Transposing is a shortcut for adding or subtracting a term from both sides. When a term is moved from one side of the equality sign to the other, its sign is reversed (+ becomes - and - becomes +).

Some equations must be simplified before they can be solved. This often involves opening brackets or clearing fractions.

To solve an equation with fractions, you can multiply both sides of the equation by the Least Common Multiple (LCM) of the denominators. This eliminates the fractions.

To remove brackets, use the distributive property. Multiply the term outside the bracket by each term inside the bracket.

After finding a solution, it is a good practice to check it. Substitute the solution back into the original equation to verify if the LHS equals the RHS.