<u>Given</u>:
(a) To determine the inequality for x for the given line.
<u>Inequality:</u>
Since, from the figure, it is obvious that the number line contains an open circle at the point 3.
This means that the end value 3 is not included in the interval.
Hence, the inequality can be written as ![x](https://tex.z-dn.net/?f=x%3C3)
Thus, the inequality for x is ![x](https://tex.z-dn.net/?f=x%3C3)
(b) <u>Given </u>that
where y is an integer.
We need to determine the possible values of y.
<u>Values of y:</u>
The values of y lie between 2 to 6. Since, the inequality is strictly lesser than, it does not contain the end value.
Therefore, the possible values of y are 3,4,5
(3) <u>Given</u> the inequality ![3 x+7>x+19](https://tex.z-dn.net/?f=3%20x%2B7%3Ex%2B19)
We need to solve the inequality.
<u>Solution:</u>
![3 x>x+12](https://tex.z-dn.net/?f=3%20x%3Ex%2B12)
![2 x>12](https://tex.z-dn.net/?f=2%20x%3E12)
![x>6](https://tex.z-dn.net/?f=x%3E6)
Thus, the solution of the inequality is ![x>6](https://tex.z-dn.net/?f=x%3E6)