We are asked to find the length of [tex]AC[/tex], which measures [tex]7x[/tex]. Using the segment addition postulate, we can add the two given expressions for [tex]AB[/tex] and [tex]BC[/tex] and make it equal to the expression for [tex]AC[/tex].
[tex]AB + BC=AC[/tex]
[tex]5x+1+15=7x[/tex]
[tex]5x+16=7x[/tex]
[tex]16=2x[/tex]
[tex]x=8[/tex]
We've found the value of [tex]x[/tex], but we aren't done yet. We need to plug in the value we got for [tex]x[/tex] into the expression for [tex]AC[/tex], which is [tex]7x[/tex]. Therefore, [tex]AC \Rightarrow7x\Rightarrow7(8)\Rightarrow\boxed{56}[/tex]. Hope this helped and have a great day!
