Question

Solve for x: 2 over 3 (x - 2) = 4x.

Answer 1

`D: x \\eq 2 \\ \\ (2)/(3(x-2))=4x \\ \\ (2)/(3x-6)=4x \\ \\ 4x(3x-6)=2 \\ \\ 12x^(2)-24x=2 \\ \\ 12x^(2)-24x-2=0 \\ \\ 6x^(2)-12x-1=0 \\ \\ \Delta=(-12)^(2)-4*6*(-1)=144+24=168 \\ \\ √(\Delta) =2 √(42) \\ \\ x_(1)= (12-2 √(42) )/(12)= (6- √(42) )/(6) \\ \\ x_(2)= (12+2 √(42) )/(12) = (6+√(42))/(6)`

Answer 2

2 / 3 ( x - 2 ) = 4x

Simplify both sides of the equation.

2/3(x−2)=4x

Simplify:

23(x−2)=4x

(2/3)(x)+(2/3)(−2)=4x(Distribute)

23x+(−4/3)=4x

Subtract 4x from both sides.

2/3x+−4/3−4x=4x−4x

−10/3x+−4/3=0

Add 4/3 to both sides.

−10/3x+−4/3+4/3=0+4/3

−10/3x=4/3

Multiply both sides by 3/(-10).

(3/−10)*(−10/3x)=(3/−10)*(4/3)

x = −2/5