To obtain the value of x, the following steps ar necessary:
Step 1: Add the lengths of the subsegments and equate to the total length of the segment, as follows:
[tex]AB+BC=AC[/tex]Since:
AB = 2x
BC = 3x + 5
AC = 40
Thus:
[tex]\begin{gathered} AB+BC=AC \\ 2x+(3x+5)=40 \\ 2x+3x+5=40 \\ 5\text{x}+5=40 \\ 5x=40-5 \\ 5x=35 \\ x=\frac{35}{5} \\ x=7 \end{gathered}[/tex]Therefore, the value of x is 7
