Question

Point B is on line segment AC and the expressions shown below represent the lengths, AB=2x, BC=3x+5, AC=40. What is the value of x.

Answer 1

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:

$AB+BC=AC$

Since:

AB = 2x

BC = 3x + 5

AC = 40

Thus:

$\begin{gathered} AB+BC=AC \\ 2x+(3x+5)=40 \\ 2x+3x+5=40 \\ 5\text{x}+5=40 \\ 5x=40-5 \\ 5x=35 \\ x=\frac{35}{5} \\ x=7 \end{gathered}$

Therefore, the value of x is 7