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Needing help to finish a rational inequality?

0 votes

(X^2−3x−10)/1−x ≥ 2

asked Jul 14, 2014 in ALGEBRA 2 by anonymous

2 Answers

0 votes

The rational inequality is image.

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.

image

image

image

image.

Now, the rational inequality is image.

  • 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 image.

image

image

image

image.

image

image

Solution of related equation is image.

  • Step - 3

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

image

answered Jul 14, 2014 by lilly Expert
0 votes

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 image True
(- 3, 1) x = 0 image False
(1, 4] x = 3 image True
(4, ∞) x = 5 image False

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

image

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  inequalityimage 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 image is { x | x ≤ - 3 and 1 < x ≤ 4 }.

answered Jul 14, 2014 by lilly Expert

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