Question 1166074
i graphed both equations and it's clear to see that 1/(x+3) is greater than 1/(-x+5) when x < 1.


here's the graph.


ddddd


solving this algebraically, i would do the following:


start with 1/(x + 3) > 1 / (-x+5)


i multiply both sides of the equation by (x + 3) to get:


1 > (x + 3) / (-x + 5)


since -x + 5 is within the parentheses, i do not reverse the inequality because i don't have -(x + 5).


in other words, if i let (-x + 5) equal to k, then the equation becomes:


1 > (x + 3) / k


i would then multiply both sides of the equation by k to get:


k > (x + 3)


since k = (-x + 5), i get:


-x + 5 > x + 3


i add x to both sides of the inequality and i subtract 3 from both sides of the inequality to get:


2 > 2x


i divide both sides of the inequality by 2 to get:


1 > x


if 1 > x, then x < 1 is my answer.


the graph confirms that.


the rules for reversing the sign of the equality are:


if you multiply both sides of the inequality by a negative number, the inequality is reversed.


you did not multiply both sides of the inequality by a negative number.

all you did was multiply both sides of the inequality by a number, that number being represented by (-x + 5).


that's not the same as multiplying both sides of the inequality by a negative number.


it's everything on each side of the inequality that has to be multiplied by a negative number that changes the sign of the inequality.