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Question 1166074: I'm trying to solve this problem, and I'm not sure if I should change the inequality sign when (-x+5) is multiplied to the numerators. (These are fractions):
1/x+3 > 1/-x+5
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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