Context: The equation $3 + \dfrac{1 - x}{7} = \dfrac{2(1 - x)}{7}$ is given, and the task is the value of $1 - x$.

Answer: 21

Why: Let $u = 1 - x$, so the equation reads $3 + \dfrac{u}{7} = \dfrac{2u}{7}$. Both fractions already share the denominator $7$, so the $u$ terms combine without any common-denominator work: subtracting $\dfrac{u}{7}$ from both sides leaves $3 = \dfrac{u}{7}$, and multiplying by $7$ gives $u = 21$. Checking, the left side is $3 + 3 = 6$ and the right side is $\dfrac{2 \cdot 21}{7} = 6$.

Common slips:

• Continuing on to $x = -20$ and reporting that; the question asks for $1 - x$, which is the quantity already found.
• Dividing by $7$ at the last step instead of multiplying gives $\dfrac{3}{7}$, undoing the fraction in the wrong direction.