Question

"Write a set of inequalities and solve to find the range of possibilities for x. You will need to write two separate inequalities instead of one compound inequality."

Answer 1

• x > 5/3
• x < 8

Explanation:

First, the side lengths should be greater than zero:

• 3x - 5 > 0
• 2x + 3 > 0

Second, The triangles have a common side and the given sides are opposite of 27° and 37° angles.

This tells us the side opposite of greater angle is greater:

• 2x + 3 > 3x - 5

Simplify each inequality:

• 3x - 5 > 0 ⇒ 3x > 5 ⇒ x > 5/3
• 2x + 3 > 0 ⇒ 2x > - 3 ⇒ x > - 3/2
• 2x + 3 > 3x - 5 ⇒ 3x - 2x < 3 + 5 ⇒ x < 8

Common solution is:

• x > 5/3
• x < 8