Graphing an Inequality on a Number Line

A number line can be used to represent the solution set of an inequality that has one variable. To graph such an inequality, first, determine its type. If it is a strict inequality, then an open boundary point is drawn. Otherwise, a closed boundary point is drawn. Then, the rest of the solution set is shaded accordingly. Consider the following inequality.

x + 2 < 8

The following four steps act as a guide in graphing the given inequality.

Determine the Type of Inequality

The first step is determining if the inequality is strict or non-strict. In this case, the given inequality is strict because the inequality symbol is

< .

Strict x + 2 < 8

Determine the Solution Set and the Boundary Point

Next, the solution set and the boundary point of the inequality need to be found. This can be done by solving the inequality using the Properties of Inequalities.

x + 2 < 8

SubIneq

$LHS - 2 < RHS - 2$

x < 6

Therefore, the boundary point is

6

and the solution set corresponds to all real numbers less than

6 .

Draw the Boundary Point on the Number Line

Here, a circle representing the boundary point is drawn on the number line. If the inequality is strict, the circle is open. If the inequality is non-strict, the circle is closed. For this example, the inequality is strict, and the boundary point is $6 .$ Then, an open circle will be drawn on the number line on the number $6 .$

Shade the Rest of the Solution Set

Finally, the rest of the solution set will be shaded by drawing an arrow that goes along the solution set and starts on the boundary point. For this situation, the solution set corresponds to all numbers less than $6,$ which means the arrow will be along the left of the boundary point.

It is worth mentioning that the graph of inequalities whose solution sets are all the real numbers are represented with bidirectional arrows that cover all the number line.

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