Answer:
[tex]x=4[/tex]
Step-by-step explanation:
The two given triangles, triangle (BDE) and triangle (BAC) share the angle (<B) in common. Moreover, their bases, line (DE), and line (AC) are parallel, this means that through the corresponding angles postulate, angles (<BDE) and (<BAC) are congrunet. Moreover, angles (<BED) and (<BCA) are also congruent. Thus, triangles (BDE) and (BAC) are similar through angle-angle similarity.
The ratio between the corresponding sides of similar triangles is the same. Therefore, one can form the following equation,
[tex]\frac{BD}{BA}=\frac{BE}{BC}[/tex].
Substitute,
[tex]\frac{BD}{BD+DA}=\frac{BE}{BE+EC}\\\\\frac{x+2}{x+x+2}=\frac{3}{3+2}[/tex]
Simplify,
[tex]\frac{x+2}{2x+2}=\frac{3}{5}[/tex]
Cross products,
[tex]5(x+2)=3(2x+2)\\[/tex]
Simplify, distribute, multiply every term inside the parenthesis by the term outside of it,
[tex]5x+10=6x+6[/tex]
Inverse operations,
[tex]5x+10=6x+6\\\\10=x+6\\\\4=x[/tex]
