The line segment HI has length 3<em>x</em> - 5, and IJ has length <em>x</em> - 1.
We're told that HJ has length 7<em>x</em> - 27.
The segment HJ is made up by connecting the segments HI and IJ, so the length of HJ is equal to the sum of the lengths of HI and IJ.
This means we have
7<em>x</em> - 27 = (3<em>x</em> - 5) + (<em>x</em> - 1)
Solve for <em>x</em> :
7<em>x</em> - 27 = (3<em>x</em> + <em>x</em>) + (-5 - 1)
7<em>x</em> - 27 = 4<em>x</em> - 6
7<em>x</em> - 4<em>x</em> = 27 - 6
3<em>x</em> = 21
<em>x</em> = 21/3
<em>x</em> = 7
