solve the folowing inequality (2x^5-4x^4-8x^3+8x^2-10x+12)/(x^4-x^3-10x^2-2x-24) is less than or equal to 0

Question

this is for pre-algebra

Answer 1

What you have here is a rational inequality.  There really not hard to solve as long as you follow these steps.

 

1) Move all terms to one side of the inequality if necessary.

 

2) Put all terms over the LCD if necessary.

 

3) Combine like terms in the numerator.  Now you have a single fraction.

 

4) Factor the numerator and denominator.

 

5) Find the zeroes of the numerator and denominator.  That is set each factor of the numerator and denominator equal to 0 and solve for x.  These values are called different names.  I call them cut-points because they cut the x-axis up into sections.

 

6) Draw a number line and plot the cut-points.  If we have ≤ or ≥ use ][ at each numerator zero.  If we have < or > use )( at each numerator zero.  The denominator zeros always get )( because we cannot divide by zero.  At the leftmost end of the number line place a ( and at the right most end place a ).  This set up allows you to write your solution in interval notation.

 

7) Test each interval by picking a test point in the interval.  Put this value back into the inequality.  You can use either the factored one or the original one.  Most students seem to use the original one.  If the test point makes the inequality true then it is part of your solution.  I like to write yes in the interval.  You can write true or even a check to let you know that interval is part of your solution.  If the test point makes the inequality not true write no, false or x.

 

8) The solution is the union of all the yeses or trues or checks.

 

I have given you the step to solve this problem.  However you state this is for pre-algebra but this is a college level problem.  Are these steps familiar to you?  If they are you will need to use a graphing calculator to get the zeros of the numerator and denominator.  Do each equation separately.  Do not enter the entire equation into the calculator.

 

The other way of doing this problem is to enter the entire equation into a graphing calculator.  The x-intervals where the graph is below the x-axis is the solution.

Answer 2

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