Answer:
x = 1 1/4
Explanation:
sqrt( 7x+2) = sqrt(3x+7)
Square each side
(sqrt( 7x+2))^2 = (sqrt(3x+7))^2
7x+2 = 3x+7
Subtract 3x from each side
7x-3x +2 = 3x+7-3x
4x+2 = 7
Subtract 2 from each side
4x+2-2 = 7-2
4x = 5
Divide by 4
4x/4 = 5/4
x = 1 1/4
Check for extraneous solution
sqrt( 7*5/4+2) = sqrt(3*5/4+7)
sqrt( 35/4 + 8/4) = sqrt(15/4+28/4)
sqrt( 43/4) = sqrt(43/4)
Solution is valid