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Answer :

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:

[tex]AB+BC=AC[/tex]

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

[tex]\begin{gathered} (2x-2)+(2x+10)=32 \\ 2x-2+2x+10=32 \end{gathered}[/tex]

Now, we can solve for x:

[tex]undefined[/tex]

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