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? (graph shown with -20, 0, 14, 20 on number line) which graph below shows the solutions? a. (graph with 0,5,10,15,20,25, 16 marked) b. (graph with 0,5,10,15,20,25, 16 open circle) d. (graph with 0,5,10,15,20,25, 18 open circle) f. (graph with 0,5,10,15,20,25, 18 marked) select your answer and then click check answer.

Explanation:

Step1: Solve the inequality

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

$$ x - 2 + 2 < 16 + 2 $$

Simplifying both sides, we get \( x < 18 \).

Step2: Analyze the error

Mason got \( x < 14 \), which suggests he subtracted 2 from 16 instead of adding 2. The correct solution is \( x < 18 \).

Step3: Identify the correct graph

We need a number line with an open circle at 18 (since the inequality is \( < \), not \( \leq \)) and the line shaded to the left of 18. Looking at the options, option F (assuming F is the one with open circle at 18 and shading left) is correct. Wait, re - checking the options: The option D? No, let's re - evaluate. Wait, the correct solution is \( x < 18 \). So the graph should have an open circle at 18 and arrow to the left. Among the given options, the one labeled F (from the user's image: "F. <---0 5 10 15 18(open circle) 20 25")? Wait, no, the user's options: Let's re - check the options as per the image. The option with open circle at 18 and shading left is the correct one. So the correct graph is the one (let's assume the last option, F, as per the user's labeling) with open circle at 18 and the line going to the left.

Answer:

The solution to the inequality \( x - 2 < 16 \) is \( x < 18 \). Mason's error was subtracting 2 from 16 instead of adding 2. The correct graph is the one with an open circle at 18 and shading to the left (e.g., option F as per the given choices).