For which values of a the system has at least one solution: 1.x≤7 ,x≥a

Given:

The system of inequalities

To find:

The values of a for which the system has at least one solution.

Solution:

We have,

    ...(i)

It means all real values of x which are less than or equal to 0.

      ...(ii)

It means all real values of x which are greater than or equal to a.

Using (i) and (ii), we get

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.

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