Respuesta :

Solve 2/3(1/4x - 2) = 1/5(4/3x - 1) for x.

The first step is the apply the Distributive Property, which is defined as a(b + c) = ab + ac. We'll apply it twice here - once for each side of the equation. Let's start with the left side.

2/3(1/4x - 2)
2/3(1/4x) + 2/3(-2)
2/12x - 4/3

Now the right side.

1/5(4/3x - 1)
1/5(4/3x) + 1/5(-1)
4/15x - 1/5

Now the equation is 2/12x - 4/3 = 4/15x - 1/5; let's solve algebraically for x.

2/12x - 4/3 = 4/15x - 1/5
2/12x = 4/15x - 1/5 + 4/3
2/12x - 4/15x = -1/5 + 4/3

Make the fractions have common denominators.

2/12x(5/5) = 10/60x
-4/15x(4/4) = -16/60x

-1/5(3/3) = -3/15
4/3(5/5) = 20/15

The equation becomes 10/60x - 16/60x = -3/15 + 20/15. Continue solving.

10/60x - 16/60x = -3/15 + 20/15
    -60/6(-6/60x) = -60/6(17/15)
                       x = -1020/90
                       x = -34/3

Answer:
x = -34/3
ACCESS MORE
EDU ACCESS