SOLUTION: Solve and write interval notation for the solution set. Then graph the solution set. 2x - 10 < - 1.4 or 2x-10 > 1.4

In this problem, you have two inequalities connected with the service word " OR ".


It means that the solution to the given system of inequalities is the UNION of solution sets for separate inequalities.


First inequality

    2x - 10 < - 1.4

implies

    2x < - 1.4 + 10  --->  2x <  8.6  --->  x < 8.6/2 = 4.3.



Second inequality

    2x - 10 > 1.4

implies

    2x > 1.4 + 10  --->  2x >  11.4  --->  x > 11.4/2 = 5.7.


Therefore, the solution of the system is the union  (-oo,4.3) U (5.7,oo).



                          The plot is shown below



     =========================|==========|===)------|-------(===|==============
     -oo                      0          4          5           6           +oo


The solution set is shown in bold.


Some parts of the plot are in scale; other parts are not.