10 points for someone who can show me how you work this algebra question out?

Question

Find the set of values of x for which 2x (squared) - 11x + 12 < 0?

Please answer it as if you were teaching someone who only knows basic algebra (such as 2x + 3x = 5 what is x)

I would really like to know how to work this out, so please basic steps.

I do not even know what this means in algebra <. I only know its "less than" but still cant understand this question.

the questiuon i am asking here is

Find the set of values of x for which 2x (squared) - 11x + 12 < 0?


and by the way its an A Level question.

Answer 1

ok first factor out that polynomial..
so... you gotta change
2x^2 - 11x +12 into
(2x-3)(x-4)
therefore
2x^2 - 11x +12 < 0 becomes
(2x-3)(x-4) < 0

this problem asks... "what number(s) can i substitiute for x that will give me an answer that is less than zero?"

right now, we've got to find the "boundary points" or points where (2x-3)(x-4) = 0, these points are important because they are the possible "end points" or "limitors" that'll give us the answer. for example, if x=1 is a boundary point, this means that the possible answers are:
a) (2x-3)(x-4) < 0 when x=1
b) (2x-3)(x-4) < 0 when x is less than 1 or
c) (2x-3)(x-4) < 0 when x is greater than 1
other possible answers ALWAYS include:
d) "does not exist" meaning (2x-3)(x-4) is never less than 0 and
e) "all real numbers" meaning (2x-3)(x-4) is always less than 0

so... for now, think of the < as an =
so...
(2x-3)(x-4) = 0
anything multiplied by 0, becomes 0 right? therefore...
(2x-3)(x-4) will be 0 when...
2x-3 = 0 or
x-4 = 0
(you have to work with these two equations now instead of one)
therefore, binary points are..
x=3/2 and x=4 or in decimals...
x=1.5 and 4

since plugging in 1.5 or 4 will make (2x-3)(x-4) EQUAL to 0 (as opposed to LESS THAN 0) you know that the possible answers do not include 1.5 or 4. in other words...
(2x-3)(x-4)<0 when..
a) x<1.5
b) x>4
c) 1.5 d) 1.5>x>4 (situation a and b)
e) does not exist

now it's time to test these points.
1)plug in ANY number less than 1.5 for x and you'll get a number GREATER than 0. this makes "situation a" impossible. since "situation d" needs "situation a and b" to be both possible, "situation d" is eliminated also.
2)plug in ANY number greater than 4 for x and you'll get a number GREATER than 0. this eliminates "situation b."
3)plug in ANY number between 1.5 and 4 for x and you'll get a number LESS than 0. the existance of such a number eliminates "situation e" and validates "situation c."

therefore... situation c is pretty much your answer.

question:
2x^2 - 11x +12 < 0
"what number(s) can i substitiute for x will give me an answer that is less than zero?"

answer:
1.5 "every number between but not including 1.5 and 4 can be substituted for x to get an anwser that is less than zero."



i want those 10 points! =)

Answer 2

ok.

firstly you need to treat it so that the < is actually a zero. it is only necessary after you find out what the function is equal to.

secondly, take the

2x^2 - 11x + 12 = 0 and factorise it, put it into two brackets that multiply to make the original.

(2x - 3) (x - 4) = 2x^2 - 11x + 12 = 0

this means that either (2x-3) = 0 or (x-4) = 0

this is because to get zero u have to multiply by 0.

thus, if x-4=0 then x = 4
and if 2x -3 = 0 then x = 3/2

these are the values you get when the function = 0

when it is less than = you're looking for the places underneath the x axis if you draw it on a graph.

this can be done easily.

to find out whether it is betwee the two values or not just put x=3 in. if this is below 0 then the answer is

2/3 < x < 4

meaning, x is greater than 2/3 but less than 4

if x= 3 is greater than 0 then

2/3 > x > 4

hope this helps

Answer 3

You do it the same way as if you had a =
-11x<12
-x<12/11

Answer 4

2x (squared) - 11x + 12 < 0
First move 12. If it's positive on one side it's negative on the other.
2x (squared) - 11x < -12
Divide by -11
2x (squared) -x < -12/11
x (squared) < -12/11

I hope this helps

Answer 5

2x (squared) -11X+12<0

-9x (Squared) + 12 < 0

-81X + 12 < 0

-81X < -12

Answer 6

You will never come upon this question in your life again. It will not pertain to your carreer. The high schools and colleges need to teach more meaningful classes. Like how to kill a terrorist, how to identify a terrorist, etc... How could that be less than zero, it does not make sense.

Answer 7

well the X is obviosely a decimal point, therefore 2. + 3. = 5

Answer 8

ok well,
2x (sq)-11x+12 is less than 0
-12 -12

= 2x(sq)-11x is less than -12

2x(sq)
-11x
=-9x is less than -12
divide both by -9 and your answer is x is less tha 1.3333.......

Answer 9

did it list the values?
there are supposed to be a few numbers that x is replaced with.
you asked this question already

Answer 10

Well then pay more attention in class and you might understand it. Not doing it for you