SOLUTION: Find the value of x that satisfies the given condition. x-4≤-6 or 2x+1≥3

We are given two inequalities

    x - 4 ≤ -6     (1)

    2x + 1 ≥ 3     (2)


connected with the servise word  " OR ".


It means that we should solve both inequalities SEPARATELY and to take the final solution as the UNION of partial solution sets.


We solve fisrst inequality

    x - 4 <= -6

    x     <= -6 + 4 

    x     <= -2.


Next we solve second inequality

    2x + 1 >= 3

    2x     >= 3 - 1

    2x     >= 2

     x     >= 1.


Now the final solution set is the union  { x <= -2 } U { x >= 1 },      ANSWER

or in the interval form                  (-oo,-2] U [1,oo).             ANSWER