Theory:

Linear equations connect the algebraic expression with another algebraic expression or numerical value with the equality sign\((=)\).
 
Let us recall some basic notations of algebraic expression:
  • A variable is a symbol for an unknown value. It is usually denoted in a letter like \(x, y, a, b,\) etc., The word 'variable' means something that can vary, i.e. change. The value of a variable is not fixed. It can take different value.
  • Constants are the terms in the algebraic expression that contain only numbers. It is constantly the same(cannot change).
    Example:
    \(4\), \(\frac{2}{7}\), \(\sqrt{5}\), \(-0.8\), etc.,
  • An algebraic expression is a mathematical expression consist of variables, constants, and the terms in the algebraic expressions are connected by operations.
    Example:
    \(2x-2\), \(2x+4\), \(4y\) etc.,
Example:
\(2x + 4\) \(=10\) is the simple linear equation.
 
Here the expressions \(2x+4\) and \(10\) are connected by equality-sign(\(=\)).
Important!
  • In a linear equation, the expression in the left-hand side (LHS) and the expression in the right-hand side (RHS) are equal.
  • The value of the variable that satisfies the equation is known as the linear equation solution.
Example:
Check whether the value given in the brackets is a solution to the given linear equation or not: \(7n + 5\) \(= 19\), \((n = 2)\).
A variable value is a solution to the given equation if LHS \(=\) RHS is replaced in the equation by the variable value.
Substitute \(n=2\) in the LHS equation, as:
 
\(7n +5\) \(=7(2)+5\) \(= 19\).
 
The LHS value is \(19\), and the RHS value is \(19\).
 
\(n=2\) is a solution to the linear equation \(7n+5\)\(=19\), since both sides are equal.