If (a - b)/b = 3/7, which of the following must also be true? | MathCelebrity Forum

If (a - b)/b = 3/7, which of the following must also be true?

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If (a - b)/b = 3/7, which of the following must also be true?

A) a/b = -4/7
B) a/b = 10/7
C) (a + b)/b = 10/7
D) (a - 2b)/b = -11/7

We can rewrite (a - b)/b as:
a/b - b/b = 3/7

Since b/b = 1, we have:
a/b - 1 = 3/7

Since -1 = -7/7, we have:
a/b - 7/7 = 3/7

Add 7/7 to each side:
a/b - 7/7 + 7/7 = 3/7 + 7/7

Cancel the 7/7 on the left side, we get:
a/b = 10/7 or Answer B

 
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