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
