How Do You Solve a Two-Step Equation by Distributing a Fraction First?

First we distribute the 2/3
Use the addition property of equality to move the 4/3
LCD stands for least common denominator
Multiply 4/1 by 3 on the top and bottom to get 12/3
Multiplying 2/3 by its reciprocal, 3/2, will cancel it out on the left hand side

1. To distribute, you'll have to multiply the 2/3 by everything inside the parentheses
2. So (2/3)•x is (2/3)x
3. And (2/3)•(-2) is -4/3
4. You'll end up with (2/3)x-4/3 on the left hand side
1. The addition property of equality says that we can add 4/3 to both sides without changing the equality
1. 4 can be represented as the fraction 4/1
2. The least common denominator is 3, so we have to change 4/1 into a fraction with a 3 in the denominator so we can add it to 4/3
3. Multiply 4/1 by 3 on both the top and bottom to get 12/3
4. 12/3 plus 4/3 is 16/3
1. A reciprocal of a fraction is the flipped version of that fraction
2. So, the reciprocal of (2/3) is (3/2)
3. If we multiply 2/3 by its reciprocal, it cancels out and leaves us with just x on the left hand side

Solve the following problem: (2/3)(x-2)=4