Here we will solve various types of problems on law of inequality.
1. Mark the statement true or false. Justify your answer.
(i) If m + 6 > 15 then m  6 > 3
(ii) If 4k >  24 then  k > 6.
Solution:
(i) m + 6 > 15
⟹ m + 6  12 > 15  12, [Subtracting 12 from both sides]
⟹ m – 6 > 3
Therefore the sentence is true.
(ii) 4k >  24
⟹ \(\frac{4k}{4}\) < \(\frac{24}{4}\), [Dividing both sides by 4]
⟹ k < 6
Therefore the sentence is false.
2. If 3z + 4 < 16 and z ∈ N then find z.
Solution:
3z + 4 < 16
⟹ 3z < 16  4, [Using the Rule of transferring a positive term]
⟹ 3z < 12
⟹ \(\frac{3z}{3}\) < \(\frac{12}{3}\), [using the Rule of division by a positive number]
⟹ z < 4
According to the given question z is natural number.
Therefore, z = 1, 2, and 3.
3. If (m – 1)(6 – m) > 0 and m ∈ N then find m.
Solution:
We know that xy > 0 then x > 0, y > 0 or x < 0, y < 0
Therefore, m – 1 > 0 and 6 – m > 0 ....................... (1)
or, m – 1 < 0 and 6 – m < 0....................... (2)
From (1) we get, m – 1 > 0 ⟹ m > 1,
and 6 – m > 0 ⟹ 6 > m
Therefore form (1), m > 1 as well as m < 6
From (2) we get, m – 1 <0 ⟹ m < 1
and 6 – m < 0 ⟹ 6 < m
Therefore form (2), m < 1 as well as m > 6
This is not possible because is m is less than 1, it cannot be greater than 6.
Thus (1) is possible and it gives 1 < m < 6, i.e., m lies between 1 and 6.
But according to the given question m is natural number. So, m = 2, 3 , 4 and 5.
`From Problems on Law of Inequality to HOME
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.