Question 1165928
{{{ (x-1)/2 + (x-6)/2 = 7 }}]
{{{ (x-1) + (x-6) = 14 }}}
{{{ 2x - 7 = 14 }}}
{{{ x = 21/2 }}}
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Check:

{{{ ((21/2)-1)/2 + ((21/2)-6)/2 = ((21/2)-(2/2))/2 + ((21/2)-(12/2))/2 = 19/4 + 9/4 = 28/4 = 7 }}} (ok)

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I wasn't sure if the 1/2's were supposed to be exponents (?)   If so, that's a different solution:
{{{ matrix(3,3,"","","", "", (x-1)^(1/2) + (x-6)^(1/2) = 7, "","","","") }}}

multiply both sides by {{{ matrix(3,3,"","","", "", (x-1)^(1/2) - (x-6)^(1/2), "","","","") }}}

(and using {{{(a+b)(a-b) = a^2-b^2 }}}...) 

{{{ matrix(3,3,"","","", "", (x-1)-(x-6) = 7((x-1)^(1/2) - (x-6)^(1/2)), "","","","") }}}<br>

{{{ matrix(3,3,"","","", "", 5/7 = (x-1)^(1/2) - (x-6)^(1/2), "","","","") }}}<br>

Add this to the very first equation to get: <br>
{{{ matrix(3,3,"","","", "", 2(x-1)^(1/2) = 54/7, "","","","") }}}<br>

and  x = 15.877551  (approx.)