Solve for x:
2.5 = 7.9 - 6 x
2.5 = 7.9 - 6 x is equivalent to 7.9 - 6 x = 2.5:
7.9 - 6 x = 2.5
Subtract 7.9` from both sides:
(7.9 - 7.9) - 6 x = 2.5 - 7.9
7.9 - 7.9 = 0:
-6 x = 2.5 - 7.9
2.5 - 7.9 = -5.4:
-6 x = -5.4
Divide both sides of -6 x = -5.4 by -6:
(-6 x)/(-6) = (-5.4)/(-6)
(-6)/(-6) = 1:
x = (-5.4)/(-6)
(-5.4)/(-6) = 0.9:
Answer: x = 0.9
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Grouping like terms, 9 x - 4 x + 1 = (9 x - 4 x) + 1:
16 = (9 x - 4 x) + 1
9 x - 4 x = 5 x:
16 = 5 x + 1
16 = 5 x + 1 is equivalent to 5 x + 1 = 16:
5 x + 1 = 16
Subtract 1 from both sides:
5 x + (1 - 1) = 16 - 1
1 - 1 = 0:
5 x = 16 - 1
16 - 1 = 15:
5 x = 15
Divide both sides of 5 x = 15 by 5:
(5 x)/5 = 15/5
5/5 = 1:
x = 15/5
The gcd of 15 and 5 is 5, so 15/5 = (5×3)/(5×1) = 5/5×3 = 3:
Answer: x = 3
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Solve for x:
5 (7 x - 2) = 60
Divide both sides of 5 (7 x - 2) = 60 by 5:
(5 (7 x - 2))/5 = 60/5
5/5 = 1:
7 x - 2 = 60/5
The gcd of 60 and 5 is 5, so 60/5 = (5×12)/(5×1) = 5/5×12 = 12:
7 x - 2 = 12
Add 2 to both sides:
7 x + (2 - 2) = 2 + 12
2 - 2 = 0:
7 x = 12 + 2
12 + 2 = 14:
7 x = 14
Divide both sides of 7 x = 14 by 7:
(7 x)/7 = 14/7
7/7 = 1:
x = 14/7
The gcd of 14 and 7 is 7, so 14/7 = (7×2)/(7×1) = 7/7×2 = 2:
Answer: x = 2
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Solve for n:
n/4 - (7 n)/8 = 1/4
Put each term in n/4 - (7 n)/8 over the common denominator 8: n/4 - (7 n)/8 = (2 n)/8 - (7 n)/8:
(2 n)/8 - (7 n)/8 = 1/4
(2 n)/8 - (7 n)/8 = (2 n - 7 n)/8:
(2 n - 7 n)/8 = 1/4
2 n - 7 n = -5 n:
(-5 n)/8 = 1/4
Multiply both sides of (-5 n)/8 = 1/4 by -8/5:
(-8 (-5) n)/(5×8) = ((-8)/5)/4
((-8)/5)/4 = (-8)/(5×4):
(-8 (-5) n)/(5×8) = (-8)/(5×4)
(-8)/8 = (8 (-1))/8 = -1:
(-5-1 n)/5 = (-8)/(5×4)
(-5)/5 = (5 (-1))/5 = -1:
--1 n = (-8)/(5×4)
(-1)^2 = 1:
n = (-8)/(5×4)
(-8)/4 = (4 (-2))/4 = -2:
Answer: n = (-2)/5
