Question

Write an inequality that represents the statement and graph the inequality. \(x\) is greater than 3 or less than \(-1\)

Short answer

The inequality that represents the statement 'x is greater than 3 or less than -1' is written as \(x > 3\) or \(x < -1\). On a graph, this is represented by two line segments on a number line, one segment to the right of 3 and the other to the left of -1, both starting with an open circle.

Step-by-step solution

Write the Inequalities

From the statement, two inequalities can be formed:1. \(x > 3\), meaning 'x' is greater than 3.2. \(x < -1\), meaning 'x' is less than -1.

Combine the Inequalities

The word 'or' in the statement implies that either condition can be true, therefore the combined inequality is \(x > 3\) or \(x < -1\).

Create the Graph

In order to represent the inequalities on a number line, draw a line and mark the points for 3 and -1. For 'x > 3', make an open circle at 3 and draw an arrow to the right to show all numbers greater than 3. For 'x < -1', make an open circle at -1 and draw an arrow to the left to show all numbers less than -1.