SOLUTION: solve and graph
{{{ 6/((x+4))+1<=4/((3x+12)) }}}.
Algebra.Com
Question 1102656: solve and graph
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Found 3 solutions by greenestamps, josgarithmetic, ikleyn:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Get all terms on one side of the inequality (with 0 on the other side), and with a common denominator.
The critical points -- where numerator or denominator are 0, and therefore the only places where the function value can change sign -- are -26/3 and -4.
Choosing test points (or any other valid method) will show that the function value is positive to the left of -26/3 and to the right of -4; it is negative only between -26/3 and -4.
If you are graphing the solution set on a number line, the left endpoint -26/3 is included in the solution set because the numerator can be 0; the right endpoint is not included because the denominator cannot be 0.
So the solution set for the inequality in interval notation is [-26/3,-4).
The solution set of the inequality can be seen in a graph of the equation:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
This is only a start - not the whole solution.
Recognize that whatever you find, .
Common denominator ;
---------------Below here is faulty because accounting for both numerator AND denominator and critical x values must be done------------------------------
recheck for any mistakes, and continue...
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
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Approach used and shown by by @josgarithmetic is W R O N G.
A V O I D it.
In the solution, you must analyse and take into account the signs of BOTH the numerator and denominator, as @greenestamps did.
Also see the lesson
- Solving inequalities for rational functions with non-zero right side
in this site.
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