Applications Of Linear Equations And Linear Inequalities In One Variable


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 If sign of linearity has been replaced by the symbol of inequality then it is called as linear inequality.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

A1X + B1X = C1 and A2X + B2X = C2 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.

Topics Covered in Applications Of Linear Equations And Linear Inequalities In One Variable

Applications of Linear Equations

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

Applications of Linear Inequalities

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

Math Topics