Question

Solve the inequality: 18 – 3(2x – 5) > 12 ; $x\in W$ .
A.{0, 1, 2, 3}
B.{3, 4, 5, 6…}
C.{1, 2, 3…..}
D.None of these

Answer 1

Hint: The given problem is related to the solution of linear inequalities. Simplify the terms on the left-hand side and the right-hand side of the inequality. Keep the variable on one side of the inequality and find the range of values for which the inequality holds.

Complete step by step answer:
Before proceeding with the solution, we have to consider that it is given that x belongs to the set of whole numbers. This means that the values that x can possess are only whole numbers. So, we can eliminate any negative numbers from being considered.
Now, coming to the given inequality, we will try to simplify the terms on both sides of the inequality and keep all the constants to one side and the variable to the other side.
We are given: 18 – 3(2x – 5) > 12
$\Rightarrow -3(2x-5)>12-18$
$\Rightarrow -3(2x-5)>-6$
Now, on shifting -3 to the right-hand side, the sign of inequality will change. So, we get:
$2x-5<\dfrac{-6}{-3}$
$\Rightarrow 2x-5<2$
$\Rightarrow 2x<2+5$
$\Rightarrow 2x<7$
\[\Rightarrow x<\dfrac{7}{2}\]
\[\Rightarrow x<3.5\]
Now, x is a whole number less than 3.5. So, x can take the values 0,1,2 and 3. So, $x\in \{0,1,2,3\}$ . Hence, option A. is the correct option.

Note: While shifting -3 to the right-hand side, most of the students forget to change the inequality sign. This is wrong and can lead to wrong answers. Whenever an inequality is multiplied or divided by a negative number, the sign of inequality changes.