Question

Sally is solving the linear equation 13 + 4x − 9 = 7x + 7 − 3x. Her final two steps are:

4 + 4x = 4x + 7
4 = 7


Select statement that correctly interprets Sally's solution.


A. The solution is x = 0


B. The solution is the ordered pair (4,7).​


C. There is no solution since 4 = 7 is a false statement.


D. There are infinitely many solutions since 4 = 7 is a false statement.

Answer 1

C. There are no solutions since 4 = 7 is a false statement.

Explanation:

Pre-Solving

We know that Sally was solving 13 + 4x - 9 = 7x + 7 - 3x, and she gets 4 = 7 at the end.

Solving

Since 4 doesn't equal 7, we know that 4 = 7 is a false statement.

We can eliminate A because if we plug 0 in as x in 4 + 4x = 4x + 7, it'll still result in 4 = 7.

We can also eliminate B since it claims that an ordered pair is the solution. We do have x in the equation, but no y value, so it's not possible for (4,7) to be the solution.
Both C and D justify the answers by using the fact that 4 = 7 is false. However, it can't be D since we already eliminated A; if at least 1 solution is wrong, then there can't be infinitely many solutions.

So, the answer is C.