Solve each inequality by graphing, using technology. Express your answer to one decimal place.
a) 2x+1/x-3 <= x
Okay, I need help solving this. Am I on the right track?
1. Make equal to zero : x- 2x+1/x-3 <= 0
2. "combine terms"? : x(x-3)-2x+1 / x-3 <= 0
............................. x^2-5x+1 / x-3 ........up to here is this correct?
3. Now I look for the "roots" or "zeros" for numerator and denominator?
....N: x can't be ____?
....D: x can't be +3.
4. Put this (your roots/zeros) on a number line. Test numbers that are in between each root on the number line?
...f(-2) (a#less than 3) = .....
...f(4) (a# greater than 3)= .....
...Is this the right process? I've been having trouble with inequalities.
Okay, here's what I did.
Numerator = 0 ->x=4.8 and x=0.2
Denominator = 0 -> x=3
Number line: |-----0.2-------3-------4.8-------|
Checked each number: 0.2 works , 3 does not work , 4.8 works.
Tested values in between each interval.
f(0.1) <=0
f(1) <=0
f(4) <=0
f(5) <=0
All integers tested between each interval were less than or equal to zero.
So then my final answer would be: (-infiniti,2) U (4, +infiniti)
Is that right?
Okay, so here is what I get now...
Numerator = 0 -> x=5.2 and x=-0.2
Denominator = 0 ->x=3
|--------(-0.2)-----------(3)----------(5.2)-----|
Test Values: (-0.2) = -0.0125 ... is Not greater than or equal to zero. *I am plugging this into "0 <= x^2-5x-1 / x-3"*
................... (3) = undefined
....................(5.2) = greater than or equal to zero.
Then pick values between each interval:
f(-1) -> 1.25 which is >= 0
f(1) -> 2.5 which is >= 0
f(4) -> -5 which is < 0
f(6) ->1.67 which is >= 0
So back to the original equation now?? ... 2x+1 / x-3 <= 0
.................................................. ......when is it less than or equal to zero?
.................................................. ......(4, 5.1)?
.................................................. ......I'm guessing the answer is wrong? Can someone please explain this to me?
Look at this solution.