From the problem, given triangle ABC is similar to triangle DEC, we can have the proportion of :
[tex]\frac{AB}{AC}=\frac{DE}{DC}[/tex]
AB = 30, AC = 2x - 1
DE = 18, DC = x + 1
This will be :
[tex]\begin{gathered} \frac{30}{2x-1}=\frac{18}{x+1} \\ \text{Cross multiply :} \\ 30(x+1)=18(2x-1) \\ 30x+30=36x-18 \\ 30x-36x=-18-30 \\ -6x=-48 \\ x=\frac{-48}{-6}=8 \end{gathered}[/tex]
The answer is x = 8
