Solving Inequations –
The steps for solving a linear inequation are similar to those for solving a linear equation.
Step.1) If there are fractions involved, multiply both sides of the inequality by the LCM of the denominators.
Step.2) Simplify both sides and separate the terms with the variable and constant terms.
Step.3) Collect the terms containing the variable on the LHS and the constants on the RHS.
Step.4) Divide both sides of the inequation by the coefficient of the variable and remember the replacement set while we are writing the solutions set.
There are some example are given below for your better understanding –
4x – 3 2x + 1
Example.1) Solve ----------- ≤ ------------, x Є W
3 5
Ans.) Multiplying both sides of the given inequation by 15 (the LCM of the denominators 3 & 5)
4x – 3 2x + 1
------------ X 15 ≤ ----------- X 15
3 5
Or, 5 (4x – 3) ≤ 3 (2x + 1)
Or, 20x – 15 ≤ 6x + 3
Or, 20x – 6x ≤ 15 + 3
Or, 14x ≤ 18
18 9
Or, x ≤ -------- = --------
14 7
9
Or, x ≤ ---------
7
But as per the given condition, x Є W ( the set of whole numbers ), so, x = whole numbers less than 9 / 7. (Ans.)