Question

let p be the solution set of 3x + 1 > x - 3 and is Q be the solution set of 5x + 2 _< 3(x + 2) x € n . find the set P intersection Q
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Answer 1

Step-by-step explanation:

Consider the first inequality

2(x−1)<3x−1

2x−2<3x−1

−1<x ...(i)

Consider the second inequality

4x−3≤8+x

3x≤11

x≤

3

11

x≤

3

9+2

x≤3+

3

2

but x is an integer

Hence, we neglect the fractional part of x.

3

2

<1, therefore

x≤3 ...(ii)

From (i) and (ii), we have

−1<x≤3

x∈(−1,3] (−1 is not included)

So, the solution set for the above inequalities is {0,1,2,3}.