Question

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

Answer 1

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]}

Answer 2

`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