Answer: (D) -3 < x < 17
Step-by-step explanation:
x must satisfy both Part 1 and Part 2 below:
Part 1: Length must be greater than 0 so:
2x + 6 > 0 and x + 23 > 0
x > -3 and x > -23
To satisfy both, x > -3
Part 2: The 80° is less than the 100° so the corresponding side of 80° must also be less than the corresponding side of 100°
80° < 100°
⇒ 2x + 6 < x + 23
x + 6 < 23
x < 17
Therefore x must be between -3 and 17
⇒ -3 < x < 17
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Answer: (C) -1.6 < y < 7
Step-by-step explanation:
y must satisfy both Part 1 and Part 2 below:
Part 1: Length must be greater than 0 so:
4y + 15 > 0 and 5y + 8 > 0
y > -3.75 and y > -1.6
To satisfy both, y > -1.6
Part 2: The 60° is less than the 105° so the corresponding side of 60° must also be less than the corresponding side of 105°
60° < 105°
⇒ 5y + 8 < 4y + 15
y + 8 < 15
y < 7
Therefore y must be between -1.6 and 7
⇒ -1.6 < y < 7
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Answer: (A) 2.4 < y < 5
Step-by-step explanation:
y must satisfy both Part 1 and Part 2 below:
Part 1: Length must be greater than 0 so:
2y + 3 > 0 and 5y - 12 > 0
y > -1.5 and y > 2.4
To satisfy both, y > 2.4
Part 2: The 70° is less than the 140° so the corresponding side of 70° must also be less than the corresponding side of 140°
70° < 140°
⇒ 5y - 12 < 2y + 3
3y - 12 < 3
3y < 15
y < 5
Therefore y must be between 2.4 and 5
⇒ 2.4 < y < 5
