document.write( "Question 1102656: solve and graph\r
\n" ); document.write( "\n" ); document.write( " $\"+6%2F%28%28x%2B4%29%29%2B1%3C=4%2F%28%283x%2B12%29%29+\"$ . \n" ); document.write( "

Algebra.Com's Answer #717352 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Get all terms on one side of the inequality (with 0 on the other side), and with a common denominator.

\n" ); document.write( " $\"+6%2F%28%28x%2B4%29%29%2B1%3C=4%2F%28%283x%2B12%29%29+\"$
\n" ); document.write( " $\"18%2F%283x%2B12%29%2B%283x%2B12%29%2F%283x%2B12%29-4%2F%283x%2B12%29%3C=0\"$
\n" ); document.write( " $\"%283x%2B26%29%2F%283x%2B12%29%3C=0\"$
\n" ); document.write( " $\"%28x%2B26%2F3%29%2F%28x%2B4%29%3C=+0\"$

\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "So the solution set for the inequality in interval notation is [-26/3,-4).

\n" ); document.write( "The solution set of the inequality can be seen in a graph of the equation:

\n" ); document.write( " $\"graph%28400%2C200%2C-30%2C10%2C-10%2C10%2C%28x%2B26%2F3%29%2F%28x%2B4%29%29\"$

\n" ); document.write( " \n" ); document.write( "

\n" );