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

Oct 4, 2016

See the explanation.

#### Explanation:

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

Add $3 x$ to both sides.

$18 < 12 + 3 x$

Subtract $12$ from both sides.

$6 < 3 x$

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

$x > 2$
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 $x \ge 2$, 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