How do you solve and graph #2/3(x-12)≤x+12#?

1 Answer
Jan 12, 2018

Answer:

#x>=-60#

Explanation:

Given:

#2/3(x-12)<=x+12#

Multiple both sides by #3#.

#2(x-12)<=3(x+12)#

Expand both sides.

#2x-24<=3x+36#

Subtract #2x# from
both sides.

#-24<=3x+36-2x#

Simplify.

#-24<=x+36#

Subtract #36# from both sides.

#-36-24<=x#

Simplify.

#-60<=x#

Switch sides.

#x>=-60#

The graph is a solid vertical line starting at #x=-60#. The solid line indicates that the graph is equal to #x=-60#. The inequality is represented by shading the graph from #x=-60# to infinity.

graph{x>=-60 [-69.35, -44.04, -2.29, 10.37]}