standard_description: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
problem_activity: Task
The following is a student solution to the inequality $$ \frac{5}{18} - \frac{x-2}{9} \leq \frac{x-4}{6}. $$ $$ \begin{align} \frac{5}{18} - \frac{x-2}{9} & \leq \frac{x-4}{6} \newline \frac{5}{18} - \frac22 \frac{x-2}{9} & \leq \frac33 \frac{x-4}{6} \newline \frac{5}{18} - \frac{2x-2}{18} & \leq \frac{3x-4}{18} \newline 5 - (2x - 2) & \leq 3x - 4 \newline 5 - 2x + 2 & \leq 3x - 4 \newline 7 - 2x & \leq 3x - 4 \newline -5x & \leq -11 \newline x & \leq \frac{11}{5} \newline \end{align} $$
There are two mathematical errors in this work. Identify at what step each mathematical error occurred and explain why it is mathematically incorrect.
The first mathematical error occurred going from line ____ to line ____.
Why it is incorrect:
The second mathematical error occurred going from line ____ to line ____.
Why it is incorrect:
How would you help the student understand his mistakes?
Solve the inequality correctly.


aligns: no