Question

this system of linear inequalities can be used to find the possible heights, in inches, of darius, \\(d\\), and his brother william, \\(w\\).

\\(d \ge 36\\)
\\(w < 68\\)
\\(d \le 4 + 2w\\)

which statements must be true about their heights? choose three correct answers.

• darius is less than 4 inches taller than twice williams height.
• darius is at most 36 inches tall.
• williams height is at least 68 inches.
• darius is no more than 4 inches taller than twice williams height.
• williams height is less than 68 inches.
• darius is at least 36 inches tall.

Explanation:

Analyze the given system of inequalities

Using the Systems of Linear Inequalities knowledge point

$$
LATEXBLOCK0
$$

Translate each inequality into verbal statements

Using the Constraint Verification knowledge point

$$
LATEXBLOCK1
$$

Evaluate the given options

Using the Constraint Verification knowledge point

• "Darius is less than 4 inches taller than twice William's height" represents \(d < 4 + 2w\), which is incorrect.
• "Darius is at most 36 inches tall" represents \(d \le 36\), which is incorrect.
• "William's height is at least 68 inches" represents \(w \ge 68\), which is incorrect.
• "Darius is no more than 4 inches taller than twice William's height" represents \(d \le 4 + 2w\), which is correct.
• "William's height is less than 68 inches" represents \(w < 68\), which is correct.
• "Darius is at least 36 inches tall" represents \(d \ge 36\), which is correct.

Answer:

• Darius is less than 4 inches taller than twice William's height.
• Darius is at most 36 inches tall.
• William's height is at least 68 inches.
• Darius is no more than 4 inches taller than twice William's height. (Correct answer)
• William's height is less than 68 inches. (Correct answer)
• Darius is at least 36 inches tall. (Correct answer)