Question

Solve : 1 ≥ 15 – 7x > 2x – 27, x ∈ N​

Answer 1

Answer:

x € { 2 , 3 , 4 }

Solution:

We have ;

1 ≥ 15 - 7x > 2x - 27 , x € N

The given inequation can be rewritten seperately as follow ↓

=> 1 ≥ 15 - 7x and 15 - 7x > 2x - 27 , x € N

=> 7x ≥ 15 - 1 and 15 + 27 > 2x + 7x , x € N

=> 7x ≥ 14 and 42 > 9x , x € N

=> 7x ≥ 14 and 9x < 42 , x € N

=> x ≥ 14/7 and x < 42/9 , x € N

=> x ≥ 2 and x < 42/9 , x € N

=> 2 ≤ x < 42/9 , x € N

=> 2 ≤ x < 4.666... , x € N

=> x € { 2 , 3 , 4 }

Hence,

The required answer is ;

x € { 2 , 3 , 4 }

Answer 2

Answer:

Here is your answer

Step-by-step explanation:

1≥15−7x≥2x−27

So we have,

1≥15−7x and 15−7x>2x−27

⇒7x≥15−1 and −2x−7x>−27−15

⇒7x≥14 and −9x>−42

⇒x≥2 and −x>−

9

42

⇒x≥2 and x<

3

14

⇒2≤x<

3

14

But as x∈N

The solution set is {2,3,4}.

Thank you

HOPE YOU UNDERSTAND ☺️