Question 1102656
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Get all terms on one side of the inequality (with 0 on the other side), and with a common denominator.<br>
{{{ 6/((x+4))+1<=4/((3x+12)) }}}
{{{18/(3x+12)+(3x+12)/(3x+12)-4/(3x+12)<=0}}}
{{{(3x+26)/(3x+12)<=0}}}
{{{(x+26/3)/(x+4)<= 0}}}<br>
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.<br>
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.<br>
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.<br>
So the solution set for the inequality in interval notation is [-26/3,-4).<br>
The solution set of the inequality can be seen in a graph of the equation:<br>
{{{graph(400,200,-30,10,-10,10,(x+26/3)/(x+4))}}}<br>