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Line segments can be split into several subsegments.
The values of x, AB and BC are 13, 10 and 20, respectively.
The given parameters are:
[tex]AB= 2x - 16[/tex]
[tex]BC= 3x - 19[/tex]
[tex]AC = 30[/tex]
The above parameters means that:
[tex]AB + BC = AC[/tex]
So, we have:
[tex]2x - 16 + 3x - 19 = 30[/tex]
Collect like terms
[tex]2x + 3x = 30 + 19 + 16[/tex]
[tex]5x = 65[/tex]
Divide both sides by 5
[tex]x = 13[/tex]
Substitute 13 for x in [tex]AB= 2x - 16[/tex] and [tex]BC= 3x - 19[/tex]
[tex]AB = 2 \times 13 - 16[/tex]
[tex]AB = 26 - 16[/tex]
[tex]AB = 10[/tex]
[tex]BC= 3x - 19[/tex]
[tex]BC= 3 \times 13 - 19[/tex]
[tex]BC= 39 - 19[/tex]
[tex]BC= 20[/tex]
Hence, the values of x, AB and BC are 13, 10 and 20, respectively.
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