First, combine the terms on the left side of the inequality while expanding the terms in parenthesis on the right side of the inequality:
#(-3 + 2.5)x <= (1.5 xx x) + (1.5 xx 4)#
#-0.5x <= 1.5x + 6#
Next, subtract #color(red)(1.5x)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:
#-color(red)(1.5x) - 0.5x <= -color(red)(1.5x) + 1.5x + 6#
#(-color(red)(1.5) - 0.5)x <= 0 + 6#
#-2x <= 6#
Now, divide each side of the inequality by #color(blue)(-2)# to solve for #x# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:
#(color(red)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(>= ) -3#
#x >= -3#
