Answer:
[tex]x=6[/tex]
Step-by-step explanation:
We have been given a triangle and we are asked to solve for x using angle bisector theorem.
Angle bisector theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side of triangle into segments that are proportional to the other two sides.
Using angle bisector theorem we can set an equation as:
[tex]\frac{4x+1}{5}=\frac{15}{3}[/tex]
Let us solve for x by multiplying both sides of our equation by 5.
[tex]\frac{4x+1}{5}*5=\frac{15}{3}*5[/tex]
[tex]4x+1=5*5[/tex]
[tex]4x+1=25[/tex]
Let us subtract 1 form both sides of our equation.
[tex]4x+1-1=25-1[/tex]
[tex]4x=24[/tex]
Upon dividing both sides of our equation by 4 we will get,
[tex]\frac{4x}{4}=\frac{24}{4}[/tex]
[tex]x=6[/tex]
Therefore, the value of x is 6 units.
