# Linear Equations And Inequalities

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An algebraic equation is a statement that the two expressions are equal. It can have one or more than one variable. An equation of the type ax + b = 0 where a not equal to 0 is called a linear equation in the variable x. A linear equation can be used to solve real world problems. Firstly we need to translate the verbal statement into mathematical statement and then solving the resulting equation.

The statement which says that one quantity is not equal to another is called an Inequation. Generally linear inequation in the variable x may be expressed as

·         ax + b is greater than or equal to 0
·          ax + b is less than or equal to 0

An Inequality is solved using the same rules as that of solving any linear equation except for multiplying or dividing by a negative number we always need to reverse the symbol of the inequality.

Example 1:

The perimeter of an equilateral triangle is 48 cm. What is the measurement of each of the sides?

Solution:

Let the length of each side be x.

Equilateral triangle has all three sides equal.

So, 3x = 48

Therefore, x = 48 / 3 = 16

Each side measures 16 cm.

Example 2:

Solve 2x + 1  <  5, x belongs to N.

Solution:

2x + 1 - 1 < 5 –1       [Subtracting 1 from both sides]

2x < 4

x < 2                          [Dividing both sides by 2]

The solution set = {1}.