Beginning Algebra With Applications, Chapter 4, 4.1, Section 4.1, Problem 26

The sum of two numbers is seven. Twice one number is four less than the other number. Which of the following equations does not represent this situation?

a.) $2n = 7-n-4$

b.) $2(7-x) = x - 4$

c.) $2x + 4 = 7 -x$

d.) $2n -4 = 7-n$

In this case, we have

$n+x = 7$

$n = 7-x \qquad$ Equation 1

And we have,

$2n = x-4 \qquad$ Equation 2

If we substitute equation 2 to 1, we get the expression written in b

$2(7-x) = x-4$

More over, if the equation 1 is to be $x=7-n$, then we obtain the expression written in a.

$2n = (7-n)-4$

$2n = 7-n-4$

Therefore, the expressions written in c and d do not represent the given situation.

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