Final answer:
The first error when solving the absolute value inequality |x-4| < 1 by graphing is potentially misinterpreting the absolute value inequality, which is Step D. The correct approach would involve separating the inequality into x < 5 and x > 3 and graphing the solution set between x = 3 and x = 5.
Step-by-step explanation:
The question concerns solving the absolute value inequality |x-4| < 1 by graphing. The first error a student might make is misinterpreting the absolute value inequality. When solving such inequalities, it is crucial to understand that the absolute value expression's range would be between -1 and 1, giving two separate inequalities to solve: x-4 < 1 and -(x-4) < 1 which simplifies to x < 5 and x > 3 respectively.
By graphing these inequalities, one should shade the region between x = 3 and x = 5 on the number line, as this represents the solution set. An error could happen at any of the following steps:
- Graphing the correct inequality if not separated into two inequalities.
- Identifying the correct solution set if the shaded area does not match the inequalities.
- Selecting the correct interval on the number line if the interval does not reflect where both inequalities are true.
The first step in which an error can be recognized would be D) Misinterpreting the absolute value inequality, as this is where a misunderstanding would lead to incorrect formations of the inequalities to be graphed.