Answer:
0 < x < 9
Step-by-step explanation:
Mary's age = x
Twice of Mary's age = 2x
Emily's age = (2x + 3) (we are told Emily is 3 years older than twice of Mary's age)
Given that the sum of their ages is > 30, we have the following expression:
[tex] (2x + 3) + x [/tex] > 30
Let's simply:
[tex] 2x + 3 + x [/tex] > 30
[tex] 3x + 3 [/tex] > 30
Subtract 3 from both sides
[tex] 3x + 3 - 3 [/tex] > [tex] 30 - 3 [/tex]
[tex] 3x [/tex] > [tex] 27 [/tex]
Divide both sides by 3
[tex] \frac{3x}{3} [/tex] > [tex] \frac{27}{3} [/tex]
[tex] x [/tex] > [tex] 9 [/tex]
Therefore, the inequality that represents Mary's possible age is: 0 < x < 9
