First, expand the term on the right side of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:
#-24r - 28 <= color(red)(-4)(5r + 4)#
#-24r - 28 <= (color(red)(-4) xx 5r) + (color(red)(-4) xx 4)#
#-24r - 28 <= -20r + (-16)#
#-24r - 28 <= -20r - 16#
Next, add #color(red)(24r)# and #color(blue)(16)# to each side of the inequality to isolate the #r# term while keeping the inequality balanced:
#color(red)(24r) - 24r - 28 + color(blue)(16) <= color(red)(24r) - 20r - 16 + color(blue)(16)#
#0 - 12 <= (color(red)(24) - 20)r - 0#
#-12 <= 4r#
Now, divide each side of the equation by #color(red)(4)# to solve for #r# while keeping the equation balanced:
#-12 /color(red)(4) <= (4r)/color(red)(4)#
#-3 <= (color(red)(cancel(color(black)(4)))r)/cancel(color(red)(4))#
#-3 <= r#
To state the solution in terms of #r# we can reverse or "flip" the entire inequality:
#r >= -3#
