SOLUTION: Solve the following inequality. 40x-84<40/x a.) Is the point x=0 included in the solution set of the inequality? b.)Are the other finite end points of the intervals included i

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Question 1065357: Solve the following inequality.
40x-84<40/x
a.) Is the point x=0 included in the solution set of the inequality?
b.)Are the other finite end points of the intervals included in the solution set?
c.) What is the solution set?

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
Posting better solution, more complete than earlier one -
-
x cannot be 0, and 0 is one of the critical x-values.

Divide both sides by 10



Concentrate on the expression on the left side






Look for the critical x-values of the numerator; the denominator has already been taken care of.

Critical x-values are and
OR after computing,
.

The three critical values cut the x-axis into four intervals on which to check for solutions.
Check within each interval using the original inequality.
Pick any value within each interval.
                                                   
pick -1                        pick -1/5                   pick 2                     pick 4

                                   

                                                      

TRUE                              TRUE                         TRUE                         FALSE

SOLUTION: The union of and
--------------------------------------------------------------------------





THIS SOLUTION POSTED EARLIER, INCOMPLETE AND WRONG:




Critical x values,



These critical x values are -2/5 and 2.5.
You will find that the solution is the x values BETWEEN BUT NOT INCLUDING -2/5 and positive 2.5.
.*
*note: because of the original inequality.

Answer by ikleyn(52847)   (Show Source): You can put this solution on YOUR website!
.
Solve the following inequality.
40x-84 < 40/x
a.) Is the point x=0 included in the solution set of the inequality?
b.)Are the other finite end points of the intervals included in the solution set?
c.) What is the solution set?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



Plots  y = 40x - 84 (red)  and  y = 40/x (green)


The inequality is hold where the red line is below  (lover than)  the green line.

The solution set is   x <  and   0 < x < 2.5.
In the interval notation the solution set is  (,) U (,).

The solution by  "josgarithmetic"  is wrong.  Ignore his writing.


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