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Inequalities question

find the set of values of x for which:
both 3(2x+1)>5-2x and 2x^2-7x+3>0

I've found the answers individualy to be x>0.25 and x<0.5 or x>3 respectively.
How do I do that bit?
Reply 1
Avatar for Notnek
Notnek
21
You need to consider both solutions of the quadratic inequality separately.

If x<0.5 then you also need x>0.25 for both inequalities to be satisfied. That means that 0.25<x<0.5 satisfies both inequalities.

What are your thoughts on the second quadratic inequality solution?
Reply 2
Avatar for raheem94
raheem94
13
Original post by bronn
find the set of values of x for which:
both 3(2x+1)>5-2x and 2x^2-7x+3>0

I've found the answers individualy to be x>0.25 and x<0.5 or x>3 respectively.
How do I do that bit?


See the below diagram:




From it we can see the range that satisfies both is 0.25<x<0.5 0.25 < x < 0.5
Reply 3
Avatar for bronn
bronn
OP
9
Original post by raheem94
See the below diagram:


From it we can see the range that satisfies both is 0.25<x<0.5 0.25 < x < 0.5


Ohhh thankyou! Just completely jogged my memory that I need to draw a diagram :smile:
Reply 4
Avatar for Notnek
Notnek
21
Original post by bronn
Ohhh thankyou! Just completely jogged my memory that I need to draw a diagram :smile:

There is another range of solutions that Raheem didn't explcitly mention. Did you get the second solution?
Reply 5
Avatar for bronn
bronn
OP
9
Original post by notnek
There is another range of solutions that Raheem didn't explcitly mention. Did you get the second solution?


No, I thought there was only one solution?! Hmm confused, help?
Reply 6
Avatar for raheem94
raheem94
13
Original post by bronn
No, I thought there was only one solution?! Hmm confused, help?


See the edited diagram:




The other range is x>3 x > 3

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