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What expressions are equal to the equation \((\frac{3}{4})x = 15\)? (Select all that apply.)

a) \(x = 20\)
b) \(x = \frac{5}{4}\)
c) \(x = \frac{60}{4}\)
d) \(x = 60\)

Answer :

Final answer:

The equation (3/4)x = 15 has only one correct solution, which is x = 20. Multiplying both sides by the reciprocal of 3/4 isolates x, showing that the other options provided are not equivalent to the original equation. Therefore, option a) x = 20 is the correct answer.

Explanation:

To solve the equation (3/4)x = 15, we need to isolate the variable x. We do this by multiplying both sides of the equation by the reciprocal of 3/4, which is 4/3. When we do that, we obtain the following:

(4/3) * (3/4)x = (4/3) * 15

This simplifies to:

x = 20

Therefore, x = 20 is the correct solution to the equation. Let's analyze the remaining options:

  • x = 5/4 is incorrect because 5/4 is not equal to 20.
  • x = 60/4 simplifies to x = 15, which is also incorrect as it does not equal 20.
  • x = 60 is incorrect because if we divide 60 by 4, we get 15, not 20.

Only option a) x = 20 is the correct expression equivalent to (3/4)x = 15.

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