b. Represent the solution set of the following on the number line.
17<2x +5 <3x + 2, x EZ
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Solution!!
17 < 2x + 5 < 3x + 2, x ∈ Z
17 < 2x + 5 | 2x + 5 < 3x + 2
17 - 5 < 2x | 5 - 2 < 3x - 2x
12 < 2x | 3 < x
12 ÷ 2 > x | 3 < x
6 > x | 3 < x
3 < x < 6 , x ∈ Z
Solution set = {4, 5}
Number line is in the attachment. The number line should be drawn using a pencil only!! Apologies for using pen!
The inequality has 3 parts so it is known as compound inequality. So, I've solved one by one taking the first and second part and then second and third part.
The sign should be reversed if doing multiplication or division.
N → Natural numbers
W → Whole numbers
I or Z → Integers
R → Real numbers
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