Question

Find the solution set of −2 ≤ 2x − 4 < 6, x ∈ N

Answer 1

Answer:

Step-by-step explanation:

If P is the solution set of −3x+4<2x−3,x∈N and Q is the solution set of 4x−5<12,x∈W, find

(i) P∩Q

(ii) Q–P

Medium

Solution

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Given inequations are,

−3x+4<2x–3 where x∈N and  

4x–5<12 where x∈W

Solving

−3x+4<2x−3

⇒−3x−2x<−3−4

⇒−5x<−7

⇒x>  

5

7

​

 

As x∈N

The solution set P is {2,3,4,5,…}

And

4x−5<12

⇒4x<12+5

⇒4x<17

⇒x<  

4

17

​

 

As x∈W

The solution set Q is {0,1,2,3,4}

Therefore,

(i) P∩Q={2,3,4}

(ii) Q−P={0,1}

Answer 2

Answer:

-2≤12-2x3<156

-2≤12-2x3 and 12-2x3<156

and

-52≤-2x3 and-2x3<86

154≥x and x > -2

3.75≥x and x > -2

since x ∈ N

∴ Solution set = {1, 2, 3}

The required graph of the solution set is: