Context: In the equation $(b - 2)x = 8$, the constant $b$ must be chosen so that the equation has no solution. A linear equation of the form $ax = c$ has no solution exactly when $a = 0$ while $c \ne 0$.

Answer: A) $2$

Why: If $b = 2$, the equation becomes $(2 - 2)x = 8$, that is, $0 \cdot x = 8$. The left side equals $0$ for every value of $x$, so it can never equal $8$, and the equation has no solution. For any other value of $b$, dividing both sides by $b - 2$ gives the single solution $x = \dfrac{8}{b - 2}$.

Traps:

• B) $4$: substituting gives $2x = 8$, which has the solution $x = 4$, so a solution exists.
• C) $6$: substituting gives $4x = 8$, which has the solution $x = 2$; the equation still has exactly one solution, not none.
• D) $10$: substituting gives $8x = 8$, which has the solution $x = 1$, so a solution exists.