We'll write the absolute values for each
term:
l 2a-5 l = 2a - 5 for 2a -
5>=0
2a >= 5
a
>= 5/2
l 2a-5 l = 5 - 2a for 2a - 5 <
0
a < 5/2
l 3a +3 l =
3a +3 for 3a +3 > = 0
3a >=
-3
a >= -1
l 3a +3 l =
-3a -3
a < -1
We'll
solve the equation considering 3 ranges of values for a:
1)
a is in the range (- infinite -1)
5 - 2a - (-3a -3) =
0
We'll remove the brackets:
5
- 2a + 3a + 3 = 0
We'll combine like
terms:
a + 8 = 0
a =
-8
Since -8 is in the range of admissible values, we'll
accept it.
2) a is in the range (- 1 ,
5/2)
5 - 2a - 3a - 3 = 0
We'll
combine like terms:
-5a = -2
a
= 2/5
Since 2/5 is in the range of admissible values, we'll
accept it.
3) a is in the range [5/2 ,
+infinite)
2a - 5 - 3a - 3 =
0
We'll combine like terms:
a
= 8
Since 8 is in the range of admissible values, we'll
accept it.
The admissible values for a are:
{-8 ; 2/5 ; 8}.
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