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3x + b = 5x - 7 3y + c = 5y - 7In the equations above, b and c are constants. ...


Question

3x + b = 5x - 7
3y + c = 5y - 7

In the equations above, b and c are constants. If b is c minus \(\frac{1}{2}\), which of the following is true?

 

Options

A)
x is y minus \(\frac{1}{4}\).
B)
x is y minus \(\frac{1}{2}\).
C)
x is y minus 1.
D)
x is y plus \(\frac{1}{2}\).

The correct answer is A.

Explanation:

Choice A is correct. Subtracting the sides of 3y + c = 5y - 7 from the corresponding sides of 3x + b = 5x - 7 gives (3x - 3y) + (b - c) = (5x - 5y) + (-7 - (-7)). Since b = c - \(\frac{1}{2}\), or b - c = -\(\frac{1}{2}\),  it follows that (3x - 3y) + (-\(\frac{1}{2}\)) = (5x - 5y). Solving this equation for x in terms of y gives x = y - \(\frac{1}{4}\). Therefore, x is y minus \(\frac{1}{4}\).

Choices B, C, and D are incorrect and may be the result of making a computational error when solving the equations for x in terms of y.


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