Question

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P is the solution set of 7x-2>4x+1 and Q is the solution set of
(9x-45)≥(x-5)

Where X∈R. Represent i) P∩Q, ii) P-Q, on a number lines and solution set.

Answer 1

Answer:

P = {x : 7x - 2 > 4x + 1, x ∈ R}

7x - 2 > 4x + 1

7x - 4x > 1 + 2

3x > 3

x > 1

and

Q = {x : 9x - 45 >= 5(x - 5), x ∈ R}

9

x

−

45

≥

5

x

−

25

9x-45≥ 5x-25

9

x

−

5

x

≥

−

25

+

45

9x-5x≥-25+45

4

x

≥

20

4x≥20

x

≥

5

x≥5

1) P ∩ Q = {x : x >= 5, x ∈ R}

2) P - Q = {x : 1 < x < 5, x ∈ R}

Step-by-step explanation:

see the attachment for number line