Answer:
x = (-2)/13
Step-by-step explanation:
Solve for x:
(2 (x - 2))/7 = 4 x
Multiply both sides by 7:
(7×2 (x - 2))/7 = 7×4 x
(7×2 (x - 2))/7 = 7/7×2 (x - 2) = 2 (x - 2):
2 (x - 2) = 7×4 x
7×4 = 28:
2 (x - 2) = 28 x
Expand out terms of the left hand side:
2 x - 4 = 28 x
Subtract 28 x from both sides:
(2 x - 28 x) - 4 = 28 x - 28 x
2 x - 28 x = -26 x:
-26 x - 4 = 28 x - 28 x
28 x - 28 x = 0:
-26 x - 4 = 0
Add 4 to both sides:
(4 - 4) - 26 x = 4
4 - 4 = 0:
-26 x = 4
Divide both sides of -26 x = 4 by -26:
(-26 x)/(-26) = 4/(-26)
(-26)/(-26) = 1:
x = 4/(-26)
The gcd of 4 and -26 is 2, so 4/(-26) = (2×2)/(2 (-13)) = 2/2×2/(-13) = 2/(-13):
x = 2/(-13)
Multiply numerator and denominator of 2/(-13) by -1:
Answer: x = (-2)/13
