Context: In $\dfrac{-20x - 47 + m}{2} = k(x + 7)$, both $k$ and $m$ are constants and the equation has infinitely many solutions. The task is the value of $m$.

Answer: A) $-93$

Why? Infinitely many solutions means the two sides are the same linear expression. The left side is $-10x + \dfrac{m - 47}{2}$ and the right side is $kx + 7k$. Matching the $x$ coefficients gives $k = -10$, so the constants must satisfy $\dfrac{m - 47}{2} = 7(-10) = -70$, hence $m - 47 = -140$ and $m = -93$.

Traps:

• B) $61$ makes the left constant $\dfrac{14}{2} = 7$ instead of $-70$, so the sides differ by a fixed amount and no solution exists.
• C) $-10$ is the value of $k$ forced by matching the $x$ terms, not the value of $m$.
• D) $23$ makes the left constant $\dfrac{-24}{2} = -12$, again short of $-70$.