Needing help to finish a rational inequality?

Question

(X^2−3x−10)/1−x ≥ 2

Answer 1

The rational inequality is .

When solving a rational inequality, begin by writing the inequality in general form with the rational expression  on the left and zero on the right.

.

Now, the rational inequality is .

• Step-1

State the exclude values, those 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 is .

• Step - 3

Draw the vertical lines at the exclude values 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 satisify the inequality.

Test interval	x - value	Inequality	Conclusion
(- ∞, -3]	x = - 3		True
(- 3, 1)	x = 0		False
(1, 4]	x = 3		True
(4, ∞)	x = 5		False

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 (- ∞, - 3] and (1, 4].

This implies that the solution  of  the  inequality is  the  interval (- ∞, - 3] and (1, 4].

Note that the original inequality contains a “ ≥ ” symbol. This means that the solution set contains the endpoints of the test interval is (- ∞, - 3] .

Solution of the inequality is { x | x ≤ - 3 and 1 < x ≤ 4 }.