Question

Solve :
⇒ 2 + 4x < 2x - 5 < 3x , x ∈ R

Answer 1

Answer:

Given inequation is,

2+4x<2x−5≤3x

⇒2+4x<2x and 2x−5≤3x

⇒4x−2x<−2 and −5≤3x−2x

⇒2x<−2 and −5≤x

⇒x<−1 and −5≤x

⇒−5≤x<−1

As x∈R

The solution set is {−5,−4,−3,−2}.

hope it helps you ✌️✅✅✅

Answer 2

Step-by-step explanation:

Given :-

• 2 + 4x < 2x - 5 < 3x , x ∈ R

To find :-

• Solution set

Solution :-

We have,

• 2 + 4x < 2x - 5 < 3x , x ∈ R

That is,

1. 2 + 4x < 2x - 5
2. 2x - 5 < 3x

Solving (1) :-

⇒ 2 + 4x < 2x - 5

⇒ 2 + 4x - 2x < 2x - 5 - 2x

⇒ 2 + 2x < -5

⇒ 2 + 2x - 2 < -5 - 2

⇒ 2x < -7

⇒ x < -7/2

⇒ x < -3.5

Solving (2) :-

⇒ 2x - 5 < 3x

⇒ 2x - 5 - 2x < 3x - 2x

⇒ -5 < x

⇒ x > -5

∴ We get :-

⇒ -5 < x < -3.5

∴ Solution set = { -5, -4 }