Which of the following is equivalent to the inequality 1/2x+1 >x answers A, 2x^2+x-1/2x+1 <0. B, 2x^2+x-1/2x+1 >0. C, 2x^2+x+1/2x+1 >0. D,2x^2+x-1 >0. E,2x^2+x+1 <0.?
1 Answer
Nov 28, 2017
Explanation:
#"given "1/(2x+1)>x#
#"express as "1/(2x+1)-x>0#
#"require fractions to have a "color(blue)"common denominator"#
#1/(2x+1)-(x xx(2x+1)/(2x+1))>0#
#rArr1/(2x+1)-(x(2x+1))/(2x+1)>0#
#rArr(1-2x^2-x)/(2x+1)>0#
#rArr-(2x^2+x-1)/(2x+1)>0larrcolor(blue)"common factor of - 1"#
#"note"#
#6>4larr"true statement"#
#"multiply both sides by "-1#
#"to correct this and make the statement true "#
#color(red)"reverse the inequality symbol"#
#rArr-6<-4larr"true"#
#"hence if we multiply/divide an inequality by a "#
#"negative value we "color(red)"reverse the symbol"#
#"we have "#
#-(2x^2+x-1)/(2x+1)>0#
#"multiply both sides by "-1#
#rArr(2x^2+x-1)/(2x+1)<0larrcolor(blue)"reverse symbol"#
