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Mathematics
Alfredo Collier
29 May, 15:20
Solve for x: 4/5 x + 4/3 = 2x
X=?
+4
Answers (
1
)
Marina Oconnell
29 May, 17:41
0
x = 10/9
Step-by-step explanation:
Solve for x:
(4 x) / 5 + 4/3 = 2 x
Put each term in (4 x) / 5 + 4/3 over the common denominator 15: (4 x) / 5 + 4/3 = (12 x) / 15 + 20/15:
(12 x) / 15 + 20/15 = 2 x
(12 x) / 15 + 20/15 = (12 x + 20) / 15:
(12 x + 20) / 15 = 2 x
Multiply both sides by 15:
(15 (12 x + 20)) / 15 = 15*2 x
(15 (12 x + 20)) / 15 = 15/15 * (12 x + 20) = 12 x + 20:
12 x + 20 = 15*2 x
15*2 = 30:
12 x + 20 = 30 x
Subtract 30 x from both sides:
(12 x - 30 x) + 20 = 30 x - 30 x
12 x - 30 x = - 18 x:
-18 x + 20 = 30 x - 30 x
30 x - 30 x = 0:
20 - 18 x = 0
Subtract 20 from both sides:
(20 - 20) - 18 x = - 20
20 - 20 = 0:
-18 x = - 20
Divide both sides of - 18 x = - 20 by - 18:
(-18 x) / (-18) = (-20) / (-18)
(-18) / (-18) = 1:
x = (-20) / (-18)
The gcd of 20 and - 18 is 2, so (-20) / (-18) = ( - (2*10)) / (2 (-9)) = 2/2 * (-10) / (-9) = (-10) / (-9):
x = (-10) / (-9)
Multiply numerator and denominator of (-10) / (-9) by - 1:
Answer: x = 10/9
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