SOLUTION: Question State the valu of x in the following inequality 3/x-4<=2/x-2 Method i have tried. Multiply both sides by the common denominator which is (x-4)(x-2) which gives

Algebra ->  Algebra  -> Inequalities -> SOLUTION: Question State the valu of x in the following inequality 3/x-4<=2/x-2 Method i have tried. Multiply both sides by the common denominator which is (x-4)(x-2) which gives      Log On

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Question 30632: Question
State the valu of x in the following inequality
3/x-4<=2/x-2
Method i have tried.
Multiply both sides by the common denominator which is (x-4)(x-2) which gives you
3(x-2)<=2(x-4) therefore
3x-6<=2x-8
bring all the variable on one side leads me to
3x-2x<=-8+6
thefore
x<=-2
Found 2 solutions by Earlsdon, Cintchr:
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
Your solution is absolutely correct and your work is impeccable!
I have one suggestion however:
When you write 3/x-4 and you really mean 3/(x-4), be sure to use parentheses, otherwise, 3/x-4 may be mistakenly construed as (3/x)-4
Good work!

Answer by Cintchr(475) About Me  (Show Source):
You can put this solution on YOUR website!
+3%2F%28x-4%29%3C=2%2F%28x-2%29+ Treat this as an equality while solving
+3%2F%28x-4%29=2%2F%28x-2%29+ since you have equivalent fractions, cross multiply
+3%28x-2%29=2%28x-4%29+ distribute
+3x-6=2x-8+ subtract 2x from both sides
+1x-6=-8+ add 6 to both sides
+x+=+-2+ since we did not multiply or divide by a negative number, put the < back in as is
+x+%3C=+-2+
You got the same answer. This is just one other way to solve the same problem.