To solve a linear equation, say 2x + 3 = 5.
What is an algebraic expression?
- Any expression involving a constant, a variable, and some operations like addition, multiplication, etc. is called an algebraic expression.
- A variable is an unknown number, and generally, it is represented by a letter like x, y, n, etc.
- Any number without any variables is called a constant.
- A number or quantity associated with a variable is called the coefficient of that variable.
- A term is any number or variable separated by operators.
Consider an expression like: 5n + 3
Fig. (1) Expression
What is linear equation?
- A linear equation is an equation in which the highest power of the variable is always 1. It could be in one variable or in two variables.
- The expressions that form the equation contain only one variable called a linear equation in one variable, i.e., the highest power of the variable appearing in the equation is 1.
- A linear equation in one variable is in the form of ax + b = 0, where a and b are any two integers and x is an unknown variable having only one solution.
Solving a Linear Equation in One Variable
A value of the variable that, when substituted for the variable in an equation, makes L.H.S. = R.H.S. and thus satisfies the equation and is called a solution of the equation.
Some Important points related to Linear Equations
- There is an equality sign in the linear equation. The expression on the left of the equal sign is called the LHS (left-hand side) and the expression on the right of the equal sign is called the RHS (right-hand side).
- In the linear equation, the LHS is equal to RHS but this happens for some values only and these values are the solution of these linear equations.
A square is a regular quadrilateral, which means that it has four equal sides and four equal angles of 90 degrees each.
Area of a Square
- The product of the length of each side itself.
- Formula: area of a square = side² = x² unit²
Fig. (2) Square
A rectangle is a four-sided quadrilateral with opposite sides that are equal and four right angles.
The dimension of a rectangle's longer side determines its length, while its shorter side determines its width.
Area of a Rectangle
- The product of its length and breadth.
- Formula: area of a rectangle = length x breadth = l x b unit²
Fig. (3) Rectangle