Question

Help With Interval Inequality?

Solve the inequality; Put the answer in interval notation . type infinity . For more than one interval use a U to represent a " union ". Write () if there is no solution.

1) 55x^2 + 26x-56<0

2) (11x+4)(5x-4)<2511

3) (3x+2)(5x-10) >55

4) (x+11) / (x-8)(x-30) ≤ 0

5) (38x-18)(x-16) / (x-35)^2 > 0

6) x / (x-9) > 342 / 71

Answer 1

6) The inequality is

• Step-1

State the exclude values,These are the values for which denominator is zero.

The exclude value of the inequality is 9.

• Step - 2

Solve the related equation

Solution of related equation

• Step - 3

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

• Step - 4

Now test  sample values in each interval to determine whether values in the interval satisify the inequality.

Test interval     x - value      Inequality                                Conclusion

(-∞, 9)               x = 8                     False

(9, 3078/271)     x = 10                   True

(3078/271, ∞)   x = 12                     False

The above conclude that the inequality is satisfied for all x - values in (9, 3078/271).

Note that the original inequality contains a “greater than” symbol. This means that the solution set does not contain the endpoints of the test interval (9, 3078/271).

The solution of the inequality is 9 < x < 3078/271

The interval notation from of solution is (9, 3078/271).