First, multiply each side of the equation by #color(red)(20)# to eliminate the fractions while keeping the equation balanced:

#color(red)(20)((x + 1)/4) = color(red)(20)(2 - ((x + 2)/5))#

#cancel(color(red)(20))5((x + 1)/color(red)(cancel(color(black)(4)))) = (color(red)(20) xx 2) - (color(red)(20) xx ((x + 2)/5))#

#5(x + 1) = 40 - (cancel(color(red)(20))4 xx ((x + 2)/color(red)(cancel(color(black)(5)))))#

#(5 xx x) + (5 xx 1) = 40 - 4(x + 2)#

#5x + 5 = 40 - (4 xx x) - (4 xx 2)#

#5x + 5 = 40 - 4x - 8#

#5x + 5 = -4x - 8 + 40#

#5x + 5 = -4x + 32#

Next, subtract #color(red)(5)# and add #color(blue)(4x)# to each side of the equation to isolate the #x# term while keeping the equation balanced:

#color(blue)(4x) + 5x + 5 - color(red)(5) = color(blue)(4x) - 4x + 32 - color(red)(5)#

#(color(blue)(4) + 5)x + 0 = 0 + 27#

#9x = 27#

Now, divide each side of the equation by #color(red)(9)# to solve for #x# while keeping the equation balanced:

#(9x)/color(red)(9) = 27/color(red)(9)#

#(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = 3#

#x = 3#