1. **State the problem:** We are given the formula $x = \frac{6a}{b - a}$ with $a = 3.46$ (3 significant figures) and $b = 6.3$ (1 decimal place). We need to find the upper bound for $x$ and give the answer correct to 3 significant figures. 2. **Understand bounds:** - For $a = 3.46$ correct to 3 significant figures, the absolute error is half the unit of the last significant figure: $\pm 0.005$. So, $a$ lies between $3.455$ and $3.465$. - For $b = 6.3$ correct to 1 decimal place, the absolute error is $\pm 0.05$. So, $b$ lies between $6.25$ and $6.35$. 3. **Find the upper bound for $x$:** Since $x = \frac{6a}{b - a}$, to maximize $x$, we want to maximize the numerator and minimize the denominator. - Maximize numerator: use the upper bound of $a = 3.465$. - Minimize denominator: minimize $b - a$ by taking the lower bound of $b = 6.25$ and the upper bound of $a = 3.465$. 4. **Calculate the upper bound:** $$ \text{Upper bound of } x = \frac{6 \times 3.465}{6.25 - 3.465} = \frac{20.79}{2.785} \approx 7.466 $$ 5. **Round to 3 significant figures:** $7.466$ rounded to 3 significant figures is $7.47$. **Final answer:** $$x_{upper} = 7.47$$