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