Solve for x: 2/7(x-2)=4x
x=2/13
x=-2/13
x=-13/2
x=13/2

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:

 x = (-2)/13

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