Question

pls awnser this question​

Answer 1

Answer :

x € [1 3⁄5 , 3)

Solution :

• Given : -x/3 ≤ x/2 - 1⅓ < 1⁄6 , x € R
• To find : Solution set

We have ;

-x/3 ≤ x/2 - 1⅓ < 1⁄6 , x € R

Here ,

Two cases arises ;

1). -x/3 ≤ x/2 - 1⅓ , x € R

and

2) x/2 - 1⅓ < 1⁄6 , x € R

Case1 :

=> -x/3 ≤ x/2 - 1⅓ , x € R

=> -x/3 - x/2 ≤ -1⅓ , x € R

=> (-2x - 3x)/6 ≤ -4⁄3 , x € R

=> -5x/6 ≤ -4⁄3 , x € R

=> 5x/6 ≥ 4⁄3 , x € R

=> x ≥ (4⁄3)•(6⁄5) x € R

=> x ≥ 8⁄5 , x € R

=> x ≥ 1 3⁄5

=> x € [1 3⁄5 , ∞)

AND

Case2 :

=> x/2 - 1⅓ < 1⁄6, x € R

=> x/2 < 1⁄6 + 1⅓ , x € R

=> x/2 < 1⁄6 + 4⁄3 , x € R

=> x/2 < (1 + 8)/6 , x € R

=> x/2 < 9⁄6 , x € R

=> x/2 < 3⁄2 , x € R

=> x < (3⁄2)•2 , x € R

=> x < 3 , x € R

=> x € (-∞ , 3)

Here ,

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

Thus ,

=> x € [1 3⁄5 , ∞) and x € (-∞ , 3)

=> x € [1 3⁄5 , ∞) ∩ (-∞ , 3)

=> x € [1 3⁄5 , 3)

Hence ,

Solution set is [1 3⁄5 , 3) .

Answer 2

Answer:

Step-by-step explanation:

x-3 and the x it =awnser