Exercise 50 Page 33

Looking at the provided work, no errors have been committed. The absolute value equation was written as two equations correctly, and inverse operations were applied correctly. However, the solutions were not checked. When solving absolute value equations, we have to check if the solutions are not extraneous.

Checking $x=\text{-}2$

Let's check if $x=\text{-}2$ satisfies the original equation. We end with a false statement, so $x=\text{-}2$ is an extraneous solution.

Checking $x=\text{-}\frac{4}{3}$

Now let's substitute $x=\text{-}\frac{4}{3}$ into the equation. Again we end with a false statement, so $x=\text{-}\frac{4}{3}$ is also an extraneous solution.