Question

Solve the following inequalities and show the solutions graphically.

(a) 5 < x + 1 < 9

(b) 3 < x + 2 < 10

(c) -1 < x + 3 < 7

Well Explained Answer Required.

Answer 1

a . 5 <x+1 <9

x <9+1- 5

x <5

b. 3 <2

Answer 2

Step-by-step explanation:

(a)

Given: 5 < x + 1 < 9

(i) 5 < x + 1

= x + 1 > 5

= x > 4

(ii) x + 1 < 9

= x < 8.

Therefore, Solution is 4 < x < 8, Interval notation is (4,8).

(b)

Given: 3 < x + 2 < 10

(i)

3 < x + 2

= x + 2 > 3

= x > 1

(ii)

x + 2 < 10

= x < 8.

Therefore,Solution set is 1 < x < 8, Interval notation is (1,8)

(c)

Given: -1 < x + 3 < 7

(i)

- 1 < x + 3

= x + 3 > -1

= x > -4

(ii)

x + 3 < 7

= x < 4

Therefore, Solution set is -4 < x < 4, Interval notation is (-4,4)

Hope it helps!