Question

question
solve for x.
answer

Explanation:

Step1: Apply the Angle Bisector Theorem

The Angle Bisector Theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the adjacent sides. So, we have the proportion $\frac{24}{10}=\frac{21}{2x - 5}$.

Step2: Cross - multiply

Cross - multiplying gives us $24(2x - 5)=10\times21$.
Expanding the left - hand side: $48x-120 = 210$.

Step3: Solve for \(x\)

Add \(120\) to both sides: $48x=210 + 120$.
So, $48x=330$.
Divide both sides by \(48\): $x=\frac{330}{48}=\frac{55}{8}=6.875$.

Answer:

\(x = 6.875\)