4) The inequality is

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• Step-1
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State the exclude values,These are the values for which denominator is zero.

The exclude value of the inequality is 8,30.

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• Step - 2
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Solve the related equation

Solution of related equation x   = -11.

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• Step - 3
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Draw the vertical lines at the exclude values and at the solution to separate the number line into intervals.

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• Step - 4
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Now test  sample values in each interval to determine whether values in the interval satisify the inequality.

Test interval   x - value      Inequality                                    Conclusion

(-∞, -11)        x =  -20     True

(-11, 8)            x = 0                   False

(8, 30)             x = 10             True

(30, ∞)           x = 35                 False

The above conclude that the inequality is satisfied for all x - values in (-∞, -11) and (8, 30).

This implies that the solution  of  the  inequalityis  the  interval (-∞, -11) and (8, 30) . as shown in Figure below. Note that the original inequality contains a “≤ ” symbol. This means that the solution set contain the endpoints of the test intervals are (-∞, 0) and(1/2, ∞)

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