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.

Consider the following inequality. x+2<8 There are four steps for 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 <. x + 2 < 8_(Strict)

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

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

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. The inequality is strict for this example, so an open circle will be drawn on the boundary point 6.

Shade the Rest of the Solution Set

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

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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