First, expand the terms in parenthesis on each side of the inequality. Be sure to handle the sign of each individual term correctly:
#(0.3 xx 9x) + (0.3 xx 7) >= 1.5 - x - 5#
#2.7x + 2.1 >= 1.5 - 5 - x#
#2.7x + 2.1 >= 1.5 - 5 - x#
#2.7x + 2.1 >= -3.5 - x#
Next, subtract #color(red)(2.1)# and add #color(blue)(x)# to each side of the inequality to isolate the #x# term while keeping the inequality balanced:
#2.7x + 2.1 - color(red)(2.1) + color(blue)(x) >= -3.5 - x - color(red)(2.1) + color(blue)(x)#
#2.7x + color(blue)(x) + 2.1 - color(red)(2.1) >= -3.5 - color(red)(2.1) - x + color(blue)(x)#
#3.7x + 0 >= -5.6 - 0#
#3.7x >= -5.6#
Now, divide each side of the inequality by #color(red)(3.7)# to solve for #x# while keeping the inequality balanced:
#(3.7x)/color(red)(3.7) >= -5.6/color(red)(3.7)#
#(color(red)(cancel(color(black)(3.7)))x)/cancel(color(red)(3.7)) >= -1.51#
#x >= -1.51# rounded to the nearest hundredth.
