Question

5.4.ps - 13 error analysis a math test asks the students to solve the inequality ( x - 3 geq 11 ), and then graph the solutions. bella said the solutions are ( x geq 8 ) and graphed the solutions as shown below. solve the inequality and graph the solutions. what error might bella have made?

Explanation:

Step1: Solve the inequality

$$x - 3 \geq 11$$
Add 3 to both sides:
$$x - 3 + 3 \geq 11 + 3$$
$$x \geq 14$$

Step2: Analyze Bella's error

Bella solved to get $x \geq 8$, which comes from incorrectly subtracting 3 from 11 instead of adding it. Her graph also incorrectly highlights values starting at 8, while the correct starting point is 14. The graph should have a closed dot at 14 and extend to the right.

Answer:

The correct solution to the inequality is $\boldsymbol{x \geq 14}$. Bella's error was subtracting 3 from 11 instead of adding 3, leading to an incorrect solution $x \geq 8$ and an incorrect graph that starts at 8 instead of 14.