Answer:
x = 10
Step-by-step explanation:
Since the line segment bisects ∠A the following ratios are equal
[tex]\frac{AB}{AC}[/tex] = [tex]\frac{x+4}{2x+1}[/tex], that is
[tex]\frac{8}{12}[/tex] = [tex]\frac{x+4}{2x+1}[/tex] ( cross- multiply )
8(2x + 1) = 12(x + 4) ← distribute both sides
16x + 8 = 12x + 48 ( subtract 12x from both sides )
4x + 8 = 48 ( subtract 8 from both sides )
4x = 40 ( divide both sides by 4 )
x = 10
