Answer: The correct option is
(D) 0 < x < 7.
Step-by-step explanation: Given that Emily is three years older than twice her sister Mary’s age and the sum of their ages is less than 30.
The age of Mary is represented by x years.
We are to select the inequality that represents Mary's possible age.
According to the given information, we have
Emily's age = (x + 3) years.
Also, since the sum of the ages of Emily and Mary is less than 30 years, so we get
(2x+3) + x < 30
⇒ 3x+3 < 30
⇒ 3x <27
⇒ x < 9.
Since the age of Mary cannot be equal to 0, so the required inequality is
0 < x <7.
Thus, option (D) is CORRECT.
