What will be the solution set of following absolute value equations and if empty set why

(i) |x+2|-3=5- |x+2|


(ii) l2y+3l /2 -3=8

(iii) ly+2l/l3l=1

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(i)            |x+2|-3 = 5- |x+2|
       |x+2| + |x+2| = 5 + 3
                 2|x+2| = 8
                   |x+2| = 4
                     x+2 = ±4
                         x = -2±4
                         x = -2+4 OR -2-4
                         x = 2, -6            ← ANSWER



(ii)    l2y+3l /2 -3 = 8
           l2y+3l /2 = 11
                l2y+3l = 22
                  2y+3 = ±22
                      2y = -3±22
                        y = (-3±22)/2
                        y = (-3+22)/2 OR (-3-22)/2
                        y = 19/2, -25/2                       ← ANSWER


(iii)    ly+2l/l3l = 1            ← note that l3l = 3
           ly+2l/3 = 1
              ly+2l = 3
                y+2 = ±3
                    y = -2±3
                    y = -2+3 OR -2-3
                    y = 1, -5                 ← ANSWER


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