Find the solution set and graph

Question

 -x+5<1/(x+3)?

Answer 1

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 -3.

• Step - 2

Solve the related equation

Roots are

• Step-3

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

Answer 2

Contd..

• Step-4

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

Test interval      x - value         Inequality                                          Conclusion

(-∞, -3)                   x =  -4                        False

(-3, -2.87)              x = -2.95      True

(-2.87, 4.87)          x = 0                              False

(4.87,∞)              x = 5                              True

The above conclude that the inequality is satisfied for all x - values in (-3, 1-√15) and (1+√15, ∞).

Solution set is -3 < x < (1-√15) and x > (1+√15).