Answer
a) $| x - 32 | = 5$ , $x = 27\%$ or $x = 37\%$
b) It does not conflict with the data.
Work Step by Step
a) The general equation of absolute value equation can be represented as $$|x - h| = d,\tag{1}$$ where $d$ is the distance from halfway point to $max$ or $min$ value and $h$ is the halfway point between the $min$ and $max$ values.
The percentage of students who voted in favor is $32\%$ subject to an error of $5\%$. So the minimum possible percentage ($5\%$ less) is $27\%$ and the maximum possible percentage($5\%$ more) is $37\%$, which makes $32\%$ the halfway point between them. Also, the distance between halfway point to either minimum or maximum value is $5\%$. Hence, the equation $(1)$ can be written $$| x - 32 | = 5.\tag{2}$$ We solve equation $(2)$.
i) Equate $x - 32$ to $5$ $$x - 32 = 5.$$ Add $32$ to both sides $$x = 37.$$
ii) Equate $x - 32$ to $-5$ $$x - 32 = -5$$ Add $32$ to both sides $$x = 27.$$ Therefore, $x = 27\%$ or $37\%$.
b) The one third of total percentage would be $\frac{1}{3} \times100$ which is $33.33\%$. From the graph, the percentage of people who voted in favor is $32\%$ (with an error of $5\%$) which makes it almost around $33.33\%$. Hence, it can be said that the classmate's claim is not conflicting with the survey data.
