If a = 1 and (a - b)/c = 1 which of the following is NOT a possible value of b?

A. -2
B. -1
C. 0
D. 1
E. 2

Equation is:

(a-b)/c = 1 where a = 1

so plug in 1 for a and look at it again

(1-b)/c = 1

now C can be anything we want, so if b = -2 we can plug it in and make it work

(1-(-2))/c = 1
3/c = 1
c = 3 and it works

HOWEVER, if we have a 0 in the numerator there isn't a number on earth that makes 0/C = 1

(1-1)/c = 1
0/c = 1
there aren't any matches for C to make this true

B cannot be 1.

Answer is D

If a=1 and (a-b)/c = 1 which of the following is NOT a possible value of b?
A. -2
B. -1
C. 0
D. 1
E. 2

First of all remember that division by zero is undefined, hence \(c\neq{0}\) and that's why you CAN cross-multiply.

\(\frac{a-b}{c}=1\) --> as \(a=1\) --> \(\frac{1-b}{c}=1\) --> \(1-b=c\), but since \(c\neq{0}\), then \(1-b\neq{0}\) --> \(b\neq{1}\).

Answer: D.

Hope it's clear.
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If a = 1, we have:

(1 - b)/c = 1

1 - b = c

We must also remember that since (1 - b)/c = 1, and since dividing by zero creates an undefined result, c cannot be zero.

Let’s test the answer choices:

A) -2

Since c = 1 - (-2) = 3, b could be -2.

B) -1

Since c = 1 - (-1) = 2, b could be -1.

C) 0

Since c = 1 - 0 = 1, b could be 0.

D) 1

Since c = 1 - 1 = 0, b cannot be 1.

Alternate Solution:

If a = 1, we have:

(1 - b)/c = 1

1 - b = c

The original equation had c in the denominator, so we know that c cannot equal 0. The value of b that makes c = 0 is b = 1. Thus, b cannot equal 1.

Answer: D
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