I'm assuming you meant to write \(7x-3\) instead... If so, \(AB=22.\)
Because \(K\) is the midpoint of \(AB,\) \(AK\) must equal \(KB.\)
Set the two equal to each other and solve for \(x\)...
\(4x+3=7x-3 \\
4x+6=7x \\
6=3x \\
x=2\)
Now plug \(2\) in for \(x\) in either \(AK\) or \(KB\).
\(AK=4(2)+3=8+3=11\)
or
\(KB=7(2)-3=14-3=11\)
Now we know half of the length of \(AB.\) Multiplying \(11\) by \(2\) will give us the full length, which is \(22.\)
