Question

A student's work on the following problem is shown. Light in the ocean will decrease with depth. The average depth for light is 600 meters, with a variance of 400 meters. Write and solve an absolute value equation to represent the depth. Step One |d – 600| = 400 Step Two d – 600 = 400 d + 600 = –400 Step Three +600 +600 –600 –600 Step Four d = 1,000 d = –200 Where did the student make their first mistake? Step One Step Two Step Three Step Four

Answer 1

The student's first mistake occurred at Step Two, where they incorrectly handled the second part of the absolute value equation. The correct approach should have resulted in two potential solutions: d = 1,000 and d = 200.

Step-by-step explanation:

The student made their first mistake at Step Two of solving the absolute value equation |d – 600| = 400. When dealing with an absolute value equation, if |x| = a, then x = a or x = –a. Thus, the correct Step Two should be:

• d – 600 = 400
• d – 600 = –400

It appears that the student correctly applied the rule to the first equation but incorrectly added 600 instead of subtracting it in the second equation, producing d + 600 = –400, which is incorrect. The proper adjustment would result in d – 600 = –400 which simplifies to d = 200 once 600 is added to both sides. This would result in two potential solutions, d = 1,000 from the first equation and d = 200 from the corrected second equation.