Final answer:
The expressions that are solutions to the equation 5 = 2/3x are options B, C, D, and E, as they represent multiplying 5 by the reciprocal of 2/3, that is 3/2, to isolate and solve for x.
Step-by-step explanation:
To solve the equation 5 = 2/3x, we need to isolate the variable x. This can be done by multiplying both sides of the equation by the reciprocal of 2/3, which is 3/2. Doing so will eliminate the fraction on the right side and give us the value of x. Let's go through each option to see if they match the solution:
- A. 5 x 2/3 - This represents multiplying 5 by 2/3, which is not the same as multiplying by the reciprocal of 2/3.
- B. 5/2/3 - This is equivalent to 5 divided by 2/3, and when we divide by a fraction, we are actually multiplying by its reciprocal; so this could be a solution.
- C. 5 divided by 2/3 - As explained for option B, dividing by a fraction is the same as multiplying by its reciprocal, making this a correct solution.
- D. 15/2 - This is the value you get when you multiply 5 (the value on the left side of the equation) by the reciprocal of 2/3, so this is the correct solution.
- E. 3/2 x 5 - This also represents multiplication of 5 by the reciprocal of 2/3, making this a correct solution.
The correct solutions that represent the value of x when 5 = 2/3x are options B, C, D, and E. The correct approach is to multiply both sides of the equation by the reciprocal of 2/3 (which is 3/2) to isolate x.