Given:
The system of inequalities
[tex]x\leq 7[/tex]
[tex]x\geq a[/tex]
To find:
The values of a for which the system has at least one solution.
Solution:
We have,
[tex]x\leq 7[/tex] ...(i)
It means all real values of x which are less than or equal to 0.
[tex]x\geq a[/tex] ...(ii)
It means all real values of x which are greater than or equal to a.
Using (i) and (ii), we get
[tex]a\leq x\leq 7[/tex]
The value of x is lies in the interval [a,7].
It means, if the value of a is less than or equal to 7, then system has at least one solution.
But if a is more than 7, then the system of inequalities have to solution.
Therefore, the value of a must be less than or equal to 7.
