Question

lim x is 5. q-√x-4 on x-5​

Answer 1

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>>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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Solution

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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<20

⇒−1≤x<5

As Q∈I

Hence, solution Q={−1,0,1,2,3,4}

The solution Q is represented on number line (b).

Therefore, P∩Q={4}

Answer 2

Answer:

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