Question

please help me!!answer this asap!!!

with step by step explanation no SPAMMING pls explain well

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Answer 1

Answer:

(i) x = { } or empty set or null set

(ii) x = {-1, 0, 1}

(iii) x = {3, 4}

(iv) x = { -3, -2, -1, 0, 1, 2, 3}

Step-by-step explanation:

(i) We know that x belongs to N, and N represents Natural Numbers

We know,

1 - 4x ⩾ -1

1 - 4x + 1 ⩾ 0

1 + 1 ⩾ 4x

2 ⩾ 4x

2/4 ⩾ x

1/2 ⩾ x

So,

x ⩽ 1/2

Thus,

x = { } or empty set or null set,

because Natural Numbers only ranges from 1 to infinity and numbers less than 1 is not a part of Natural numbers

(ii) x belongs to Z, where Z represents integers

Now,

-3 ⩽ 4x + 1 < 9

Lets take,

-3 ⩽ 4x + 1

-3 - 1 ⩽ 4x

-4 ⩽ 4x

-4/4 ⩽ x

-1 ⩽ x

Also,

4x + 1 < 9

4x < 9 - 1

4x < 8

x < 8/4

x < 2

Thus,

-1 ⩽ x < 2

and x = {-1, 0, 1}

(iii) x belongs to W, where W represents whole numbers

Now,

0 < 2x - 5 < 5

Let's take,

0 < 2x - 5

5 < 2x

5/2 < x

2.5 < x

Also,

2x - 5 < 5

2x < 5 + 5

2x < 10

x < 10/2

x < 5

Thus,

2.5 < x < 5

x = {3, 4}

x is not equal to 2.5 because 2.5 is not a part of whole numbers

(iv) x belongs to Z, where Z belongs to integers

Now,

-3 < (x/2) - 1 < 1

Let's take

-3 < (x/2) - 1

-3 + 1 < x/2

-2 < x/2

-4 < x

Also,

(x/2) - 1 < 1

x/2 < 1 + 1

x/2 < 2

x < 4

Thus,

-4 < x < 4

So,

x = { -3, -2, -1, 0, 1, 2, 3}

Hope it helped and you understood it........All the best