document.write( "Question 496151: Solve the inequality. Graph the solution set and write it in interval notation.\r
\n" ); document.write( "\n" ); document.write( "x(1-6x)<-2 \n" ); document.write( "
Algebra.Com's Answer #336406 by lwsshak3(11628)\"\" \"About 
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Solve the inequality. Graph the solution set and write it in interval notation.
\n" ); document.write( "x(1-6x)<-2
\n" ); document.write( "**
\n" ); document.write( "x(1-6x)≤-2
\n" ); document.write( "x-6x^2≤-2
\n" ); document.write( "x-6x^2+2≤0
\n" ); document.write( "multiply by (-1) and reverse inequality sign
\n" ); document.write( "6x^2-x-2≥0
\n" ); document.write( "(2x+1)(3x-2)≥0
\n" ); document.write( "number line:
\n" ); document.write( "<.....+.....-1/2]....-....[2/3....+......>
\n" ); document.write( "Interval notation:
\n" ); document.write( "(-∞,-1/2] U [2/3, ∞)
\n" ); document.write( "..
\n" ); document.write( "Explanation for signs in number line:
\n" ); document.write( "When x>2/3, the function>0
\n" ); document.write( "When going left thru the zeros, 2/3 and -1/2, the sign will switch if the zero is of an odd multiplicity, ie, 1,3,5, etc. The sign will not switch going thru a zero of even multiplicity like 2 or 4.
\n" ); document.write( "Zeros of given problem are of multiplicity 1, so the sign switches. Math teachers usually use charts to do this, but I have found this method to be a lot faster and simpler. \n" ); document.write( "
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