Question

find the solution set of each of the following inequations in the given domain x + 12 < 4x - 2, x e n

Answer 1

Answer:

3x-7> x + 1

3x 7+7>x+1+7 3x > x + 8 3x-x>x+8 -x 2x > 8 Divide both sides by 2, we get 2x/2> 8/2 The solution of the given inequation is (4,0).

X>4

5. x+5> 4x-10 Solution:

Given: x + 5> 4x - 10

x+5-5> 4x-10-5

x > 4x - 15

4x-15 < x

3x - 15 <0

4x 15 x < X-X 3x 15+15 <0 + 15 Divide both sides by 3, we get 3x/3 < 15/3

3x < 15

X<5

The solution of the given inequation is (-∞, 5).

6. 3x +92-x+ 19

Solution: Given: 3x +92-x+19 3x +9-92-x+19-9 3x2-x + 10 3x + x2-x + 10 + x 4x2 10 Divide both sides by 4, we get

4x/42 10/4

x ≥ 5/2 : The solution of the given inequation is [5/2, 0).

7. 2 (3-x) 2 x/5 +4 Solution: