Question

if the replacement set is the set of natural numbers, solution set of -3=< 1/2 - 2x/3 < 1 1/6 is?​

Answer 1

Answer: Replacement Set: The set, from which the values of the variable which involved in the inequation, are chosen, is known as replacement set.

But, if the replacement set is the set of real numbers, the solution set can only be described in set-buider form, i.e., {x : x ∈ R and y < 6}.

Solved example on replacement set and solution set in set notation:

1. If the replacement set is the set of whole numbers (W), find the solution set of 4z – 2 < 2z + 10.

Solution:

4z – 2 < 2z + 10

⟹ 4z – 2 + 2< 2z + 10 + 2, [Adding 2 on both the sides]

⟹ 4z < 2z + 12

⟹ 4z – 2z < 2z + 12 – 2z, [Subtracting 2z from both sides]

⟹2z < 12

⟹ 2z2 < 122, [Dividing both sides by 2]

⟹ z < 6

Since the replacement set = W (whole numbers)

Therefore, the solution set = {0, 1, 2, 3, 4, 5}

2. If the replacement set is the set of real numbers (R), find the solution set of 3 - 2x < 9

Solution:

3 - 2x < 9

⟹ - 2x < 9 – 3, [by transferring 3 on the other side]

⟹ -2x < 6

⟹ −2x−2 > 6−2, [Dividing both sides by -2]

⟹ x > -3

Since the replacement set = R (real numbers)

Therefore, the solution set = {x | x > -3, x ∈ R}.

3. If the replacement set is the set of integers, (I or Z), between -6 and 8, find the solution set of 15 – 3d > d - 3

Solution:

15 – 3d > d - 3

⟹ 15 – 3d - 15 > d – 3 – 15, [Subtracting 15 from both sides]

⟹ -3d > d - 18

⟹ -3d - d> d – 18 – d, [Subtracting d from both sides]

⟹-4d > -18

⟹ −4d−4 < −18−4, [Dividing both sides by -4]

⟹ d < 4.5

Since, the replacement is the set of integers between -6 and 8

Therefore, the solution set = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4}

10th Grade Math