Construction of linear equation — lesson. Mathematics State Board, Class 7.

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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 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:

$7n +5$

$=7(2)+5$

$= 19$ .