Explanation:
Square both sides of the equation to get
2x-7 = 1
2x = 8
x = 4 put '4' into the original equation to see if it works
sqrt(2(4) - 7) = 1 ?
sqrt (1) = 1 Yes so it is not extraneous
(x ^(1/6) )^3 multiply the exponents to get
x ^ 3/6 = x ^ 1/2 = sqrt x