First, subtract #color(red)(150)# and #color(blue)(0.5x)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:
#5x + 150 - color(red)(150) - color(blue)(0.5x) >= 0.5x + 105 - color(red)(150) - color(blue)(0.5x)#
#5x - color(blue)(0.5x) + 150 - color(red)(150) >= 0.5x - color(blue)(0.5x) + 105 - color(red)(150)#
#(5 - color(blue)(0.5))x + 0 >= 0 - 45#
#4.5x >= -45#
Now, divide each side of the inequality by #color(red)(4.5)# to solve for #x# while keeping the inequality balanced:
#(4.5x)/color(red)(4.5) >= -45/color(red)(4.5)#
#(color(red)(cancel(color(black)(4.5)))x)/cancel(color(red)(4.5)) >= -10#
#x >= -10#
