Question

Solve: 1<3(x-2) + 4 ≤ 10, X E N.​

Answer 1

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>>Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation

>>If P is the solution set of - 3x + 4 <

Question

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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}