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Simplify: 3a - [(4 - 3a)/5] - [(a - 4)/6]

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lucky092569 | Honors

Posted January 6, 2011 at 1:04 AM via web

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Simplify: 3a - [(4 - 3a)/5] - [(a - 4)/6]

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3 Answers | Add Yours

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted January 6, 2011 at 1:11 AM (Answer #1)

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We have to simplify : 3a - [(4 - 3a)/5] - [(a - 4)/6]

3a - [(4 - 3a)/5] - [(a - 4)/6]

Open the brackets

=> 3a - [4 /5 - 3a/5] - [a/6 - 4/6]

=> 3a - 4/5 + 3a/5 - a/6 + 4/6

add terms with a and the numeric terms

=> 3a + 3a/5 - a/6 - 4/5 + 4/6

=> 103a/30 - 2/15

Therefore 3a - [(4 - 3a)/5] - [(a - 4)/6] = 103*a/30 - 2/15

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giorgiana1976 | College Teacher | Valedictorian

Posted January 6, 2011 at 1:14 AM (Answer #2)

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We'll multiply all terms by the LCD = 5*6 = 30

[30*3a - 6(4 - 3a) - 5(a-4)]/30

We'll remove the brackets:

(90a - 24 + 18a - 5a + 20)/30

We'll combine like terms inside brackets:

(103a - 4)/30

The simplified expression is

(103a - 4)/30.

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neela | High School Teacher | Valedictorian

Posted January 6, 2011 at 1:32 AM (Answer #3)

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To simplify: 3a - [(4 - 3a)/5] - [(a - 4)/6].

We begin from the inner bracket first:

3a - [4/5 -3a/5]  - [a/6-4/6]

= 3a  -4/5 -(-3a/5) -a/6 -(-4/6)

= 3a-4/5+3a/5-a/6+4/6

= 3a+3a/5-a/6 -4/5+4/6

= a(3+3/5-1/6) - 4/5+4/6

= a{3 + (3*6-1*5)/30} + (-4*6+4*5)/30)

= a{3+13/30} -4/30

= 103a/30 -4/30

= 103a/30 -2/15.

Therefore  3a - [(4 - 3a)/5] - [(a - 4)/6] = 103a/30 - 2/15.

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