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Find all values of t such that \(6t - \frac23 + \frac{t}{5} = 4 + \frac{2-t}{3}\).

If you find more than one answer, enter every answer you find as list separated by commas.

 Aug 20, 2020
edited by Creampuff  Aug 20, 2020
 #1
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t = 64/79.

 Aug 20, 2020
 #2
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thats incorrect

Creampuff  Aug 20, 2020
 #3
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6 t - 2/3 + t/5 = 4 + (2 - t)/3 
Solve for t:
(31 t)/5 - 2/3 = (2 - t)/3 + 4

Put each term in (31 t)/5 - 2/3 over the common denominator 15: (31 t)/5 - 2/3 = (93 t)/15 - 10/15:
(93 t)/15 - 10/15 = (2 - t)/3 + 4

(93 t)/15 - 10/15 = (93 t - 10)/15:
1/15 (93 t - 10) = (2 - t)/3 + 4

Put each term in (2 - t)/3 + 4 over the common denominator 3: (2 - t)/3 + 4 = 12/3 + (2 - t)/3:
(93 t - 10)/15 = 12/3 + (2 - t)/3

12/3 + (2 - t)/3 = ((2 - t) + 12)/3:
(93 t - 10)/15 = (-t + 2 + 12)/3

Grouping like terms, -t + 2 + 12 = (12 + 2) - t:
(93 t - 10)/15 = ((12 + 2) - t)/3
279t - 30 =210 - 15t
279t + 15t =210 + 30
294t = 240
t =240 / 294


t =40 / 49

 Aug 20, 2020

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