Question

solve for the inequality 3x-2/x-4 greater than or equal to 0..help please.

Answer 1

Do you mean
\[\frac{ 3x - 2 }{ x - 4 } \ge 0\]

Answer 2

yes..

Answer 3

whoa hold the phone

Answer 4

there is a big mistake here

Answer 5

you cannot multiply by any expression with a variable, because you don't know it it is positive or negative
lets start again

Answer 6

\[\frac{ 3x - 2 }{ x - 4 } \ge 0\] numerator changes sign at \(\frac{2}{3}\) denominator changes sign at \(4\)

Answer 7

break up the real line in to three intervals
\[(-\infty,\frac{2}{3}),(\frac{2}{3},4),(4,\infty)\]

Answer 8

your expression will change signs at each of these intervals. it will be positive, then negative, then positive

Answer 9

you can check the sign by replacing \(x\) by any number you choose in any interval
for example if \(x=0\) then you get \(\frac{-2}{-4}=\frac{1}{2}\) which means it is positive on the interval containing 0, namely
\[(-\infty,\frac{2}{3})\]

Answer 10

so it is positive on \((-\infty, \frac{2}{3})\) negative on \((\frac{2}{3},4)\) and then positive again on \((4,\infty)\)

Answer 11

you want positive, or more correctly "greater than or equal to zero" so pick
\[(-\infty, \frac{2}{3}]\cup (4,\infty)\]

Answer 12

4 is "open" because the denominator cannot be zero, \(\frac{2}{3}\) is closed because that is when the expression is equal to zero

Answer 13

be careful with these, it is tempting to multiply by the denominator to clear the fractions, but you cannot do that. again the reason is that you do not know if it is positive or negative, so you do not know whether to change the inequality or not

Answer 14

Thanks satellite73. You are correct. I solved it like an equation instead of an inequality. I've removed my incorrect answer, so it'll be less confusing. I just left my first question on top to clear up what the problem reads like.

Answer 15

okay..thanks satellite73. && also thank you mathstudent55 for helping also. ya are the best (: