Simultaneous Solution of Inequalities of the form x>a and x≤b

Q. The minimum speed with which any vehicle can travel on the road is 20 kmph and the maximum speed limit is 60 kmph. Express this relation in the form of an inequality if the speed of the vehicle is represented by S.

1. $20<S\le 60$
   
2. $20<S<60$
   
3. $20\le S\le 60$
   
4. $20\le S<60$
   

Q. If $x$ is a positive integer and the range of $x$ is represented on the number line.Find out the possibles value(s) of $x$?

1. -4
2. 0
3. 1
4. 4

Q. Oliver had a total of 12 books. He decided that he would read more than 4 books in next month, but no more than eight. Which of following group of inequalities best reflects Oliver's reading habits? (Assume Oliver read $N$ number of books in the month)

1. $N>4$ and $N\le 8$
2. $N>4$ and $N<8$
3. $N\ge 4$ and $N<8$

Q. John is making the guest list for his birthday party. He can afford more than 6 person and atmost upto 11. Express this in terms of inequality. If the number of guests is represented by N.

1. $6<N\le 11$
2. $6<N<11$
3. $11<N\le 6$
4. $6\le N\le 11$

Q. Which of the following number line represents $t>0$ and $t\le 4$?
Note: In a number line, a closed circle on the number gets included in the solution, while an open circle on the number will not get included in the solution

1. 
2. 
3. 
4. 

Q. Express $y>-2$ and $y\le 2$ into a compound inequality.

1. $-2<y\le 2$
2. $-2\le y\le 2$
3. $-2<y<2$

Q. The number $7$ lies in the compound inequality $1<N<16.$

1. True
2. False

Q. Express $y>-1$ and $y\le 3$ as a compound inequality.

1. $-1<y<3$
   
2. $-1<y\le 3$
   
3. $-1\le y\le 3$
   
4. $-1\le y<3$