Will you specify in which applet you have used the execute command Execute({"{" + (Take(Sum(Sequence("," + (l1(j)), j, 1, 3)), 2)) + "}"})?

Or please share the link to the applet and the object name.

Actually, I need the list of inequalities to update itself whenever I change the whole list of inequalities, even when there is more or a lesser number of inequalities in the list of text of inequalities.

I have tried a lot to get a solution to this puzzle. Here is a version I have tried but it has limitations on getting into my purpose:

l1 = {"x<-3", "-3<=x<-1", "-1<=x<1", "1<=x"}

In a Checkbox with the name "Execute" I have added the following GeoGebra scripts:

Execute[l1]

SetVisibleInView[a,1,false]

SetVisibleInView[a,2,false]

SetVisibleInView[b,1,false]

SetVisibleInView[b,2,false]

SetVisibleInView[c,1,false]

SetVisibleInView[c,2,false]

SetVisibleInView[d,1,false]

SetVisibleInView[d,2,false]

SetVisibleInView[lintervals,1,false]

SetVisibleInView[lintervals,2,false]

SetValue[Execute,true]

SetValue[Stop,false]

Delete[e]

Delete[i]

Delete[j]

Delete[k]

SetValue[lintervals,RemoveUndefined({a,b,c,d})]

and in a Checkbox with the name "Stop" added the GeoGebra scripts; a, b, c, and d are used because these are the names the resulting objects take when the text list is executed:

SetValue[Stop,true]

SetValue[Execute,false]

Delete[a]

Delete[b]

Delete[c]

Delete[d]

I need to get the resulting objects into a list before/without naming/making them.

So, I tried

l2 = Zip(Execute Element(l1, i), i, 1…Length(l1)) or

l3 = Zip(Element({Execute l4}, i), i, 1…Length(l4))

Without the Checkbox with aforementioned scripts I got the result: {null, null, null, null}

With the Checkbox with scripts, the result are:

{"truex<-3", "true-3<=x<-1", "true-1<=x<1", "true1<=x"} when checked

and

{"falsex<-3", "false-3<=x<-1", "false-1<=x<1", "false1<=x"} when unchecked.

Please see my trial: https://www.geogebra.org/classic/d8js6txp