If x E{-2,-1,0,1,2,3,4,5}, find the solution set of each of the following inequations: (i) 3x + 4 < 15 (i) 2/3 +x - 1/6
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Answers
Answer:
Explanation:
Explanation:
We are given two inequalities which has the solution that belongs to { -2, -1, 0, 1, 2, 3, 4, 5 }
Inequality (i)
⇒ 3x + 4 < 15
⇒ 3x < 11
⇒ x < 11/3
⇒ x < 3.666...
Which means every value of x which is less than 3.6 satisfies the given inequality, but it is given in the question that x must belong to the given set of solutions.
So, We have the following solution
⇒ x ∈ { -2, -1, 0, 1, 2, 3 }
Inequality (ii)
⇒ 2/3 + x < 1/6
⇒ x < 1/6 - 2/3
⇒ x < (1 - 4)/6
⇒ x < -3/6
⇒ x < -0.5
Which means every value of x less than -0.5 satisfies the given inequality. But x must belong to { -2, -1, 0, 1, 2, 3, 4, 5 }, so we have
⇒ x ∈ {-2, -1}
Some Information :-
☞ A set is a collection of objects or item, that are of the same type, like Set of Integers, Set of all Cities, Set of all countries, e.t.c
☞ The number of Subsets of a set can be given by 2^{n} where n is the number of elements in the set.
⇒ 3x + 4 < 15
⇒ 3x < 11
⇒ x < 3.666...
⇒ x ∈ { -2, -1, 0, 1, 2, 3 })
⇒ 2/3 + x < 1/6
⇒ x < -3/6
⇒ x < -0.5