Given:
(a) To determine the inequality for x for the given line.
Inequality:
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 [tex]x<3[/tex]
Thus, the inequality for x is [tex]x<3[/tex]
(b) Given that [tex]2<y<6[/tex] where y is an integer.
We need to determine the possible values of y.
Values of y:
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) Given the inequality [tex]3 x+7>x+19[/tex]
We need to solve the inequality.
Solution:
[tex]3 x>x+12[/tex]
[tex]2 x>12[/tex]
[tex]x>6[/tex]
Thus, the solution of the inequality is [tex]x>6[/tex]
