Question

Which one of the following satisfy the
inequality 2x -- 3 > 5? The domain is
* Integers
4, 5, 6, 7 O
5,6,7,8
1, 2, 3, 4 O
2,3,4,5 O​

Answer 1

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>Maths

>Linear Inequalities

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

>Given: P = {x : 5 < 2x - 1 ...

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Given: P={x:5<2x−1≤11,x∈R}  and  Q={x : −1≤3+4x<23,x∈I} where R = (real numbers), I = (integers)

Represent P and Q on the number line. Write down the elements of P∩Q.

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Given, P={x : 5<2x−1≤11,x∈R}  and  Q={x : −1≤3+4x<23,x∈I}

Solving for P,

5<2x−1≤11

⇒5+1<2x≤11+1

⇒6<2x≤12

⇒3<x≤6

Hence, P={x : 3<x≤6,x∈R}

The solution P is represented on number line (a).

Next, solving for Q

−⇒1≤3+4x<23

⇒−1−3≤4x<23−3

⇒−4≤4x<2