Write inequality in interval notation, and graph the interval. See Examples 1, 2, and 3.Ex...

Write inequality in interval notation, and graph the interval. See Examples 1, 2, and 3.

Example 1 Graphing an Interval on a Number Line

Graph x > -5.

The statement x > -5 says that x can represent any value greater than -5 but cannot equal -5, written (-5, ∞). We graph this interval by placing a parenthesis at -5 and drawing an arrow to the right, as in Figure The parenthesis at -5 indicates that -5 is not part of the graph.

Figure Graph of the interval (-5, ∞)

Example 2 Graphing an Interval on a Number Line

Graph 3 > x.

The statement 3 > x means the same as x<3. The inequality symbol

continues to point to the lesser value. The graph of x<3, written in interval notation as (-∞, 3), is shown in Figure.

Figure Graph of the interval (-∞, 3)

Example 3 Graphing a Three-Part Inequality

Write the inequality -3 ≤ x<2 in interval notation, and graph the interval.

The statement is read “-3 is less than or equal to x and x is less than 2.” We want the set of numbers that are between -3 and 2, with -3 included and 2 excluded. In interval notation, we write [ -3, 2), using a square bracket at -3 because -3 is part of the graph and a parenthesis at 2 because 2 is not part of the graph. See Figure.

Figure Graph of the interval [-3, 2)