Question

Find the range of possible measures of x if each set of expressions represents measures of the sides of a triangle.

Answer 1

• C. x > 3/2

Explanation:

According to the triangle inequality theorem, any side length is less than the sum of the other two:

• x < 2x + 1 + x + 4 ⇒ x < 3x + 5 ⇒ 2x > - 5 ⇒ x > - 2.5
• 2x + 1 < x + x + 4 ⇒ 2x + 1 < 2x + 4 ⇒ 1 < 4, any value of x
• x + 4 < x + 2x + 1 ⇒ x + 4 < 3x + 1 ⇒ 2x > 3 ⇒ x > 3/2

Common solution of the three inequalities above is:

• x > 3/2

Correct choice is C