(x-3)/(x+1)>=0

Question

Express solution using interval notation. Step by step please..?

Answer 1

The rational inequality is

• Step-1

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

The exclude value of the inequality is -1.

• Step - 2

Solve the related equation

Solution of related equation x   = 3.

• Step - 3

Draw the vertical lines at the exclude value 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

(-∞, -1)             x =  -2                   True

(-1, 3)                x = 2               False

(3, ∞)                x = 4                    True

Note that the original inequality contains a “ ≥ ” symbol, We inlude it into set of solutions at x  = 3.

Above statement is true.

x  = 3 is a solution of inequality.

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

Solution of the inequality

x  < - 1

x  ≥ 3

The interval notation form of inequality is (-∞, -1) U [3, ∞).