Question

Please solve diz question...

Answer 1

Answer:

Step-by-step explanation:

I can only type a response, so for the "represent on the number line" part, I'll just have to describe it in words.  I hope that this is not a problem for you.

a) 3 - x > -2  =>  3 > x - 2  =>  5 > x  =>  x < 5

Also, x ∈ N says x is a natural number, so x is among the numbers 1, 2, 3,...

Putting the two together, x must be one of the number 1, 2, 3, 4.

Represent on the number line:  Just fill in dots at the numbers 1, 2, 3 and 4

b) 10 - 2 ( 1 + 4x ) < 20  =>  10 < 20 + 2 ( 1 + 4x )  =>  10 - 20 < 2 + 8x

=> -10 -2 < 8x  =>  -12 < 8x  => -3/2 < x  =>  x > -3/2.

It says also x ∈ I.  I don't know that your set "I" is, but I suspect it is just meant to mean the set of integers, so the same thing as "Z" in (f).  These are the numbers ... -3, -2, -1, 0, 1, 2, 3,...

Putting the two together, x must be one of the numbers -1, 0, 1, 2, 3, 4, 5,...

Represent on number lines:  Fill in dots at -1, 0, 1, 2, 3, 4, 5,... as far as your line goes to the right.  Be sure to NOT put dots at -2, -3, -4, ...

c) 2x - 3 > 2  =>  2x > 5  =>  x > 5/2.  Again, x ∈ N.  Putting these two together, x must be one of the numbers 3, 4, 5, 6, ...

Represent:  Fill in dots at 3, 4, 5, 6, ... as far as you can to the right.  Be sure to NOT put dots left of 3.

d) 1 - 3x ≤ 5x + 17  => 1 - 17 ≤ 5x + 3x  =>  -16 ≤ 8x  =>  -2 ≤ x.  Again, x ∈ I, which I'm taking to mean the same as x ∈ Z.  (If you have a special meaning for I in your class, you'll have to make the necessary change, sorry.)

Putting this together, x must be one of the numbers -2, -1, 0, 1, 2, 3,...

Represent:  Dots at -2, -1, 0, 1, 2, 3,... as far right as you can.  Be sure to NOT put dots left of -2.

e)  11 ≤ 3x + 5 ≤ 17  =>  11 - 5 ≤ 3x ≤ 17 - 5  =>  6 ≤ 3x ≤ 12  =>  2 ≤ x ≤ 4

Also, x ∈ N.  Together, x must be one of the numbers 2, 3, 4.

Represent:  Dots at 2, 3 and 4 only.

f)  -3 < x/2 - 1 < 1  =>  -3 + 1 < x/2 < 1 + 1  =>  -2 < x/2 < 2  =>  -4 < x < 4.

Together with x ∈ Z (x is an integer), this means x must be one of the number -3, -2, -1, 0, 1, 2, 3.

Represent:  Dots at these 7 places only.

g) 2x - 2 ≤ 16 - x < 3x - 2

First bit says:  2x - 2 ≤ 16 - x  =>  2x + x ≤ 16 + 2  => 3x ≤ 18  =>  x ≤ 6

Second bit says:  16 - x < 3x - 2  =>  16 + 2 < 3x + x  =>  18 < 4x  =>  18 / 4 < x  => x > 18/4 = 4.5

So x > 4.5 and x ≤ 6.  Together with x ∈ I (again, x ∈ Z ?) , this means x must be one of the numbers 5, 6.

Represent:  Dots at 5 and 6 only.