Question

URGENT- PLEASE DO THIS SUM ​

Answer 1

Question:

Solve the given inequation :

2x - 1 ≥ x + (7-x)/3 > 2 , x € R .

Also , graph the common solution set .

Answer:

Solution set : x € [5/2,∞)

(For graphical representation of solution set, please refer to the attachment)

Solution:

The given inequation is;

2x - 1 ≥ x + (7-x)/3 > 2 , x € R .

Here , two cases arises;

Case1 : 2x - 1 ≥ x + (7-x)/3

Case2 : x + (7-x)/3 > 2

Case1 :

=> 2x - 1 ≥ x + (7-x)/3

=> 2x - 1 - x ≥ (7-x)/3

=> x - 1 ≥ (7-x)/3

=> 3•(x - 1) ≥ 7 - x

=> 3x - 3 ≥ 7 - x

=> 3x + x ≥ 7 + 3

=> 4x ≥ 10

=> x ≥ 10/4

=> x ≥ 5/2

=> x € [5/2,∞)

Case2 :

=> x + (7-x)/3 > 2

=> (7-x)/3 > 2 - x

=> 7 - x > 3•(2-x)

=> 7 - x > 6 - 3x

=> 3x - x > 6 - 7

=> 2x > -1

=> x > -1/2

=> x € (-1/2,∞)

The solution set of the given inequation will be given as the intersection set of case1 and case2.

Thus;

Solution set will be;

x € [5/2,∞)n(-1/2,∞)

x € [5/2,∞)

Hence,

Common solution set is ;

x € [5/2,∞) .