Question

Plz answer thr ques correctly⇪​

Answer 1

Answer:

OPTION A BRO CORRECT

ND THIS IS BEFORE ONE

Answer 2

Answer :

(i). (1 , 9)

Solution :

• Given : |x - 4| < 5 and |2x + 5| > 7
• To find : Common solution set

Note :

• If |x| = a , then x = ± a

• If |x| < a , then x € (-a,a) [ OR -a < x < a ]

• If |x| > a , then x € (-∞,-a) U (a,∞)

[ OR x < -a or x > a ]

Here ,

We need to find common solution set for

1). |x - 4| < 5

and

2). |2x + 5| > 7

Case1 : |x - 4| < 5

=> |x - 4| < 5

=> -5 < x - 4 < 5

=> -5 + 4 < x < 5 + 4

=> -1 < x < 9

=> x € (-1,9)

AND

Case2 : |2x + 5| > 7

=> |2x + 5| > 7

=> 2x + 5 < -7 or 2x + 5 > 7

=> 2x < - 7 - 5 or 2x > 7 - 5

=> 2x < -12 or 2x > 2

=> x < -12/2 or x > 2/2

=> x < -6 or x > 1

=> x € (-∞,-6) U (1,∞)

Here ,

The solution set of given system of inequations will be given as the intersection set of solutions found in both the cases .

Thus ,

Solution set will be given as ;

=> x € (-1,9) and x € (-∞,-6) U (1,∞)

=> x € (-1,9) ∩ [ (-∞,-6) U (1,∞) ]

=> x € (1,9) [ OR 1 < x < 9 ]

Hence ,

The solution set is (1 , 9) .