Question

given line segmebt that contains the points A,B & C in order, if AB=2x-2,and BC=2x+10, and AC=32, find x

Answer 1

We have a segment with 3 points. The complete segment goes from A to C, and point B divides it in 2 sibsegments (AB and BC)

Note that segment AC is composed by those 2 subsegments, so its complete legth will be equal to the sum of the leghts of subsegments AB and BC. Then, we can build the following equation:

`AB+BC=AC`

As we know the lengths in terms of x, we just need to replace in the previous equation:

`\begin{gathered} (2x-2)+(2x+10)=32 \\ 2x-2+2x+10=32 \end{gathered}`

Now, we can solve for x: