Question

Write an inequality that represents the statement and graph the inequality. \(x\) is greater than 7 or less than 5 .

Short answer

The inequality is \(x > 7\) or \(x < 5\). The graph is a number line with an open interval towards the right from 7 and an open interval towards the left from 5.

Step-by-step solution

Convert the statement into an inequality

The given statement is 'x is greater than 7 or less than 5'. We can write this as an inequality: \(x > 7\) or \(x < 5\).

Graph the inequality

We graph this inequality on a number line. Let us draw a continuous number line and mark the points at 5 and 7. Since it is mentioned that x is greater than 7, we place an open circle on 7 and draw the line towards the right to depict \(x > 7\). Similarly, we place an open circle on 5 and draw the line towards the left to represent \(x < 5\). The open circles on 5 and 7 represent that these numbers are not part of the solution. Hence, this graph represents all the numbers that are less than 5 and greater than 7.