Linear inequality is a combination of linear expression and an inequality. An inequality is represented by sign of 'greater than' (>), 'less than' (<), greater than and equal to (≥) or less than equal to (≤).Linear inequality may contain two or more inequalities in a single expression. If sign of linearity has been replaced by the symbol of inequality then it is called as linear inequality. Lets consider a function f (x), then relation of natural numbers ’n’ with function f (x) can be expressed by inequality as shown below:
f (y) > n or f (y) ≥ n.
For instance consider the following equation 2x + 10 > 50.
In above equation symbol of inequality is used and hence it shows linear inequality. A linear equation can be defined as the first order differential equation, these equations are of first degree. Such as
A_{1}X + B_{1}X = C_{1} and A_{2}X + B_{2}X = C_{2} represents two linear equations with two unknowns.
Lets try to explain Applications of Linear Equations and Linear Inequalities in One Variable using following examples:
Y + 5 > 0,
Then adding - 5 both sides gives
Y + 5 - 5 > 0 – 5,
Y > - 5. This is the required solution which expresses linear inequality.
To understand solution of linear equation, lets take two equations as:
4a + 3b = 10 and 6a – 3b = 40 then to solve these equations we have to add them, we get
10a = 50 which gives a = 5,
Substituting the value of 'a' in first equation, we get:
4 * (5) + 3b = 10,
3b = 10 – 20 = -10,
b = -10/3.
Linear equation is an algebraic expression having both constants and variables. Linear expression is an expression which contains (=) sign and highest degree is one, like x +2, x + 5y etc. Number of variables in an equation may be one or more than one. It is possible to convert a non - linear equation into linear equation. Here we will discuss...Read More
Linear inequality includes a linear function and an inequality. An inequality is obtained when two expressions are connected by the sign of 'greater than' or 'less than'. It is actually a system with just two or more inequalities together. Linear inequality is similar to the linear function if the sign of linearity replaces the symbol of in...Read More