### 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.