a=?Find possible a values if  |2a-5|- |3a +3| = 0

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation |2a-5|- |3a +3| = 0 has to be solved.

|2a-5|- |3a +3| = 0

=> |2a-5| = |3a +3|

This gives:

2a - 5 = 3a + 3

=> a = -8

2a - 5 = -3a - 3

=> 5a = 2

=> a = 2/5

The possible values of a are (-8 , 2/5)

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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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