Question

error analysis a math test asks the students to solve the inequality x - 2 < 16, and then graph the solutions. mason said the solutions are x < 14 and graphed the solutions as shown below. solve the inequality and graph the solutions. what error might mason have made? -20 0 14

Explanation:

Step1: Solve the inequality

To solve \( x - 2 < 16 \), add 2 to both sides of the inequality.
\( x - 2 + 2 < 16 + 2 \)
\( x < 18 \)

Step2: Analyze Mason's error

Mason got \( x < 14 \) instead of \( x < 18 \). It seems he subtracted 2 from 16 (i.e., \( 16 - 2 = 14 \)) instead of adding 2 to 16. For the graph, the correct graph should have an open circle at 18 (since the inequality is strict, \( x < 18 \)) and the arrow pointing to the left (towards smaller numbers) from 18. Mason's graph has the open circle at 14, which is incorrect because the correct solution is \( x < 18 \).

Answer:

The solution to the inequality \( x - 2 < 16 \) is \( x < 18 \). Mason's error was likely in solving the inequality (he probably subtracted 2 from 16 instead of adding 2) and thus graphed the solution at \( x < 14 \) instead of \( x < 18 \). The correct graph should have an open circle at 18 with an arrow pointing to the left.