math

posted by .

how do you solve this inequality
3x-2 < x+4/x-2
please help i don't get it

  • math -

    You must mean:
    3x-2 < (x+4)/(x-2) , so clearly x ≠ 2
    (x-2)(3x-2) < x+4
    3x^2 - 8x + 4 - x - 4 < 0
    3x^2 - 9x < 0
    3x(x-3) < 0

    So the "critical values" are x=0 , x = 2, and x=3

    test for a value of x<0
    let x=-5 in original
    -17 < -1/-7
    -17 < 1/7 ? YES

    test for a value between 0 and 2
    let x=1
    1 < 5/-1
    1 < -5 ? NO

    test for a value between 2 and 3
    let x = 2.5
    5.5 < 6.5/.5
    5.5 < 13 ? , YES

    test for a value x>3
    let x=5
    13 < 9/3
    13 < 3 ? , NO

    so we have x ≤ 0 OR 2 < x ≤ 3 , notice that x=2 in not included

    To see that this is correct
    go to my favourite graphing program
    http://rechneronline.de/function-graphs/
    and enter
    3x-2 - (x+4)/(x-2)

    in the window for "first graph"
    change the "Range y-axis from" entries to -200 to 200

    you will see the curve below the x-axis from -infinitity to 0
    above the x-axis from 0 to the asymptote of 2
    below the x-axis from 2 to 3, and
    above the x-axis for x>3

  • math -

    thanks so much :)

  • math -

    what if all the values you put in do not work. how would you write the intervals.?

  • math -

    If the inequality can not be satisfied for any real value of x, then you just have to say that.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra 2(check) cont..

    1)solve the inequality -3(r-11)+15>_9 my answer = r<_13 2)solve the inequality -2<4z+10<_12 my answer = -3<z<_1/2 3)solve the inequality 2x-5<_10 or 33-4x<5 my answer is x<_15/2 or <7 4)solve the inequality …
  2. algebra II

    14. Solve the inquality -3(r-11) + 15 equal or greater than 9. 15.Solve the inequality: -2 < 4z = 10 lessthan or equal to 12. 16. Solve the inequality 2x-5 less than or equal to 10 or 33 - 4x < 5 17. Solve the inequality 3 | …
  3. Pre-Algebra

    Can someone please show me how to solve these problems step-by-step so that I can understand how to do them?
  4. math

    Please solve -2x+7>22 -2x+7-7>22-7 -2x>15 -2x/(-2)<15/(-2) Switching the order of the inequality here is essential to keep the solutions true for the inequality since I divided by a negative #. x<-7.5
  5. 8th grade math for Ms. Sue

    How is an inequality different from an equation?
  6. algebra 2

    the 2 unequalities -26<4k-2 and 2k-1<6 A. Write a compound inequality to combine the inequalities shown previously. and B. Solve the compound inequality for values of k. Show your work. Write your final answer as one inequality. …
  7. equations & inequalities

    1.simplify this expression 4p+9+(-7p)+2=?
  8. Math ~CHECK MY WORK~

    With stars are my answers. Please check them if they are wrong please tell me the right ones. Number 1 (the bottom one) I don't get it so please help me with that one please! 1) You have $60 in your wallet and want to buy some new …
  9. Math

    Mr.jacobs budgeted $1,200 for tiles. His sketch of the floor requires him to use 38 white tile. each white tile cost $12. Write and solve an inequality to find the maximum amount he can spend on his brown tile. I'm not sure how to …
  10. Please Math

    8. p + 4 < –24 p < –20 p < 28 p < –28 p < 20 9.p/8 ≥ –5 p ≥ 40 p ≥ 3 p ≥ –13 p ≥ –40 10. –5p > –30 p > 6 p < 6 p > –35 p < 35 11. Which inequality matches …

More Similar Questions