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

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

This is what I got

X = 15.33