In Example 2, change the > to 5. By using Eq. (17.1), we have 2x 1

In Example 2, change the > to <, solve the resulting inequality, and graph the solution.

Data from Example 2

Solve the inequality |2x − 1| > 5.
By using Eq. (17.1), we have 2x − 1 < −5 or 2x − 1 > 5 Completing the solution, we have

This means that the given inequality is satisfied for x < −2 or for x > 3. [We must  be very careful to remember that we cannot write this as 3 < x < −2.] The solution is shown in Fig. 17.31.

The meaning of this inequality is that the numerical value of 2x − 1 is greater than 5. By considering values in these intervals, we can see that this is true for values of x less than −2 or greater than 3.

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2.x < 4 or 2x > 6 x<-2 x > 3