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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 $$\frac{1}{2}$$.

### 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.