How do you solve #18-3x<12# and graph the solution on a number line?

2 Answers
Oct 4, 2016

Answer:

See the explanation.

Explanation:

Solve and graph: #18-3x<12#

Add #3x# to both sides.

#18<12+3x#

Subtract #12# from both sides.

#6<3x#

Divide both sides by #3#.

#2< x#

Switch sides.

#x>2#

Graph a dashed vertical line at #x=2#. This indicates that the vertical line at #x=2# is not part of the graph. Shade in the area to the right of the dashed line to represent all numbers greater than #2#.

graph{x>2 [-10, 10, -5, 5]}

Oct 4, 2016

Answer:

#x> 2#
On the number line, an open circle is drawn on 2 with a ray drawn to the right.

Explanation:

Follow the same method as explained by Maeve60 to solve the inequality as
#x > 2#

There are two types of graphs that can be drawn for inequalities:

  • The 2-dimensional graph on a set of axes as shown in the other answer
  • A - 1-dimensional number line graph.

For this graph, an OPEN circle is drawn at 2 to indicate that 2 is NOT included in the solution, because #x# has to be BIGGER than 2.
A ray is then drawn extending to the RIGHT indicating all the possible values of #x# as the solution.

Note that:

  • an open circle on a number line graph becomes a dashed line on a 2 -D graph, and a ray becomes a shaded area.

  • If the solution had been #x>= 2#, then a FULL or CLOSED dot would be used on the number line graph, and a SOLID line would be drawn on the x-y graph