Question

kyle asks his friend jane to guess his age and his grandmothers age. kyle says his grandmother is not more than 80 years old. he says his grandmothers age is, at most, 3 years less than 3 times his own age. jane writes this system of inequalities to represent k, kyles age, and g, kyles grandmothers age. inequality 1: g > 80 inequality 2: g ≤ 3k - 3 which inequality did jane write incorrectly, and how could it be corrected? inequality 1 is incorrect; it should be g ≤ 80. inequality 1 is incorrect; it should be g ≥ 80. inequality 2 is incorrect; it should be g < 3k - 3. inequality 2 is incorrect; it should be g ≥ 3k - 3.

Explanation:

Step1: Analyze Inequality 1

Kyle states his grandmother is not more than 80, meaning her age $g$ is less than or equal to 80. Jane wrote $g > 80$, which is the opposite. The correct inequality is $g \leq 80$.

Step2: Analyze Inequality 2

Kyle says his grandmother's age is at most 3 years less than 3 times his age ($3k - 3$). "At most" translates to $\leq$, so Jane's $g \leq 3k - 3$ is correct.

Answer:

Inequality 1 is incorrect; it should be $g \leq 80$.