Linear Inequations

       
           

In algebra mathematics a Linear inequation is defined as an inequality which contains a linear function. When two expressions are connected to each other by 'greater than' or 'less than' sign with sign of inequality then we get inequality expression. Inequality function provides us facility to check or to make a comparison between greater and smaller quantity.

When we work on inequalities in terms of real numbers, linear inequalities are the ones written in form of following types:
f (x) < a,
or
f (x) ≤ a,
Here f (x), is a linear function in real numbers and (a) is a constant real number. Alternatively, above can be represented as:
g (x) < 0 or g (x) ≤ 0,
Here g (x) is an affine function.

Above expressions are generally written as following equation:
a0 + a1 x1 + a2 x2 + a3 x3 + a4 x4 + ……. + an xn < 0,
or
a0 + a1 x1 + a2 x2 + a3 x3 + a4 x4 + ……. + an xn ≤ 0,

Linear inequality is the combination of variable, constant and operation with inequality signs like the > (greater than), < (lesser than), ≥ (greater than or equal to) and ⩽ (lesser than or equal to), here maximum power of variable is one and degree of linear inequality is also one.
Procedure of Solving Linear Inequalities is similar to solving linear equations. While solving Linear Inequations our main aim is to move variables on one side of inequality and numbers on other side.
If we have a Linear Inequation,
2x – 4 ≤ 0?
Then we can determine the solution for the above Linear Inequation.
Given that 2x – 4 ≤ 0
We have, 2x - 4 ≤ 0
Adding 4 on both sides of the above Linear Inequations, we get:
(2x – 4) + 4 ≤ + 4,
2x ≤ 4,
Dividing 2 on both sides of above Linear Inequation, we get:
2x/2 ≤ 4/2,
x ≤ 2,
Hence, any real number less than or equal to 2 is solution of the given inequation 2x – 4 ≤ 0.
The solution set of the given in equation is (-∞, 2].

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