First, add #color(red)(7)# to each side of the equation to isolate the radical term while keeping the equation balanced:
#5root(3)(5q - 3) - 7 + color(red)(7) = -22 + color(red)(7)#
#5root(3)(5q - 3) - 0 = -15#
#5root(3)(5q - 3) = -15#
Next, divide each side of the equation by #color(red)(5)# to isolate the radical while keeping the equation balanced:
#(5root(3)(5q - 3))/color(red)(5) = -15/color(red)(5)#
#(color(red)(cancel(color(black)(5)))root(3)(5q - 3))/cancel(color(red)(5)) = -3#
#root(3)(5q - 3) = -3#
Then, cube each side of the equation to eliminate the radical while keeping the equation balanced:
#(root(3)(5q - 3))^3 = -3^3#
#5q - 3 = -27#
Next, add #color(red)(3)# to each side of the equation to isolate the #q# term while keeping the equation balanced:
#5q - 3 + color(red)(3) = -27 + color(red)(3)#
#5q - 0 = -24#
#5q = -24#
Now, divide each side of the equation by #color(red)(5)# to solve for #q# while keeping the equation balanced:
#(5q)/color(red)(5) = -24/color(red)(5)#
#(color(red)(cancel(color(black)(5)))q)/cancel(color(red)(5)) = -24/5#
#q = -24/5# or #q = -4.8#
