Question

find the range of possible values for x.
(4x - 10)
120° 24
115°
40
24
x >

Explanation:

Step1: Identify triangle with 120° angle

Two sides: 24, 24. Use triangle inequality: $(4x-10) < 24+24$ and $(4x-10) > |24-24|$.
So $4x-10 < 48$ → $4x < 58$ → $x < 14.5$; $4x-10 > 0$ → $4x >10$ → $x>2.5$.

Step2: Check 115° triangle validity

Two sides: 40,24. Their triangle is valid (40<24+24? No, wait: 40<24+third side? No, the 115° triangle has sides 40,24, and the shared side (same as 120° triangle's other side? No, focus on the side $(4x-10)$ being positive first from Step1's lower bound.

Step3: Confirm positive length constraint

The side $(4x-10)$ must be positive, so $4x-10>0$ → $x>2.5$. The upper bound from triangle inequality is $x<14.5$, but the question only asks for $x>$ value, so take the lower bound.

Answer:

2.5