Context: The number $y$ is $84$ less than the number $x$, and we must pick the equation that represents this relationship.

Answer: D) $y = x - 84$

Why: "$84$ less than $x$" is the value obtained by subtracting $84$ from $x$, which is $x - 84$. Since $y$ equals that quantity, the equation is $y = x - 84$. Check with numbers: if $x = 100$, then $y$ should be $100 - 84 = 16$, and the equation gives exactly that.

Traps:

• A) $y = x + 84$: adds instead of subtracting, which would make $y$ equal to $84$ more than $x$.
• B) $y = \dfrac{1}{84}x$: treats "less than" as if it meant dividing $x$ into $84$ parts; the phrase signals subtraction, not division.
• C) $y = 84x$: turns "$84$ less than" into "$84$ times," multiplying instead of subtracting.