Question

Solve the following in equation and represent the solution set on the number line3x/5+ 2 < x + 4 ≤ x/2+5,x€R​

Answer 1

Step-by-step explanation:

ANSWER

Take the first inequality:

4x−19<

5

3x

−2⇒20x−95<3x−10⇒17x<85

⇒x<5...(1)

Now tale the second inequality:

5

3x

−2≤−

5

2

+x⇒3x−10≤−2+5x⇒−8≤2x

⇒x≥−4...(2)

From (1) and (2)

−4≤x<5

Answer 2

Answer :

• x € (-5 , 2] ( ie. –5 < x ≤ 2 , x € R )

• For representation of solution set on number line , please refer to the attachment.

Solution :

• Given : 3x/5 + 2 < x + 4 ≤ x/2 + 5 , x € R

• To find : Solution set

We have ,

3x/5 + 2 < x + 4 ≤ x/2 + 5 , x € R

Case 1 :

=> 3x/5 + 2 < x + 4 , x € R

=> x + 4 > 3x/5 + 2 , x € R

=> x - 3x/5 > 2 - 4 , x € R

=> (5x - 3x)/5 > -2 , x € R

=> 2x/5 > -2 , x € R

=> x > -2•(5/2) , x € R

=> x > -5 , x € R

=> x € (-5 , ∞)

Case 2 :

=> x + 4 ≤ x/2 + 5 , x € R

=> x - x/2 ≤ 5 - 4 , x € R

=> (2x - x)/2 ≤ 1 , x € R

=> x/2 ≤ 1 , x € R

=> x ≤ 1•2 , x € R

=> x ≤ 2 , x € R

=> x € (∞ , 2]

→ Here , the intersection set of case1 and case2 will give the solution set .

Thus ,

Solution set will be given as ;

→ x € (-5 , ∞) and x € (∞ , 2]

→ x € (-5 , ∞) ∩ (∞ , 2]

→ x € (-5 , 2] ( ie. –5 < x ≤ 2 , x € R )

Hence ,

Solution set : x € (-5 , 2]

( ie. –5 < x ≤ 2 , x € R ) .