Question

replacement set {0,1,2,3,4,5,6,7}
find the solution set :☝️
plz help to solve it​

Answer 1

Answer:

» -2x + 7/2 < ½

» -2x < 1/2 - 7/2

» -2x < -6/2

» -2x < - 3

» x > 3

Therefore, solution set is {4, 5, 6, 7}.

Answer 2

• 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}

• 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}.

• 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}