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Directions:Solve the nonlinear inequality. Express the solution using interval notation. (If you need to use - or , enter -INFINITY or INFINITY.)
(3)/(x-1) - 4/x greater than or equal to 1
2007-09-09 13:29:27 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
3/(x-1) - 4/x ≥ 1
3x/[x(x-1)] - 4(x-1)/[x(x-1)] ≥ 1
[-x + 4]/[x(x-1)] ≥ 1
[-x + 4]/[x(x-1)] - [x(x-1)]/[x(x-1)] ≥ 0
[-x² + 4]/[x(x-1)] ≥ 0
[(2+x)(2-x)]/[x(x-1)] ≥ 0
we have critical points (x-intercepts) at 2 and -2, and critical points (vertical asymptotes) at 0 and 1. for x in (-∞,-2), inequality is false, but true for x in [-2,0). test x = -1 and get 1.5. false for x in (0,1), true in (1,2], false in (2,∞). just test 1 number in each interval. so solution is [-2,0) U (1,2].
2007-09-09 14:27:32 · answer #1 · answered by Philo 7 · 0⤊ 0⤋
given x² - 5x + 6 > zero we get (x-two)(x-three) > zero then we will see that x<>two and x <> three <----one million----?----?----four----> so scan a quantity not up to two, among two and three, and larger then three one million move two.five fail four move then we've so x
2016-09-05 08:18:15 · answer #2 · answered by ? 4 · 0⤊ 0⤋