we have
-------> inequality 1
or
-------> inequality 2
we know that
In this system of inequalities, for a value to be the solution of the system, it is enough that it satisfies at least one of the two inequalities.
let's check each of the values
<u>case 1)</u> x=-6
<u>Substitute the value of x=-6 in the inequality 1</u>
-------> is ok
The value of x=-6 is a solution of the compound inequality-----> It is not necessary to check the second inequality, because the first one satisfies
<u>case 2)</u> x=-3
<u>Substitute the value of x=-3 in the inequality 1</u>
-------> is ok
The value of x=-3 is a solution of the compound inequality-----> It is not necessary to check the second inequality, because the first one satisfies
<u>case 3)</u> x=0
<u>Substitute the value of x=0 in the inequality 1</u>
-------> is not ok
<u>Substitute the value of x=0 in the inequality 2</u>
--------> is not ok
The value of x=0 is not a solution of the compound inequality
case 4) x=3
<u>Substitute the value of x=3 in the inequality 1</u>
-------> is not ok
<u>Substitute the value of x=3 in the inequality 2</u>
--------> is ok
The value of x=3 is a solution of the compound inequality
case 5) x=8
<u>Substitute the value of x=8 in the inequality 1</u>
-------> is not ok
<u>Substitute the value of x=8 in the inequality 2</u>
--------> is ok
The value of x=8 is a solution of the compound inequality
<u>case 6)</u> x=10
<u>Substitute the value of x=10 in the inequality 1</u>
-------> is not ok
<u>Substitute the value of x=10 in the inequality 2</u>
--------> is ok
The value of x=10 is a solution of the compound inequality
therefore
<u>the answer is</u>
[-6,-3,3,8,10]