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Inequalities

Find the set values of x for wich,

BOTH 3(2x+1)>5-2x AND 2x^2 -7x+3>0
Original post by Beechey23
Find the set values of x for wich,

BOTH 3(2x+1)>5-2x AND 2x^2 -7x+3>0


You need to solve both inequalities separately, then compare the results and determine the set of values of x that satisfies both of them. Post your working if stuck.
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Beechey23
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Original post by old_engineer
You need to solve both inequalities separately, then compare the results and determine the set of values of x that satisfies both of them. Post your working if stuck.

Yeah I know I have to solve them and that's where I am alright it's just because it says the both, and I didn't really understand that bit
Original post by Beechey23
Yeah I know I have to solve them and that's where I am alright it's just because it says the both, and I didn't really understand that bit

Let's say you has two inequalities, with respective solutions x >1 and x < 5. The set if values of x that satisfies both those inequalities is then 1 < x < 5. (x has to be both greater than 1 AND less than 5).
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Beechey23
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Original post by old_engineer
Let's say you has two inequalities, with respective solutions x >1 and x < 5. The set if values of x that satisfies both those inequalities is then 1 < x < 5. (x has to be both greater than 1 AND less than 5).

IMG_20191130_142037.jpgI've done that and part C is what we have been talking about I've found the set values for both inequalities but now I've got part C which is where I'm stuck
Original post by Beechey23
I've done that and part C is what we have been talking about I've found the set values for both inequalities but now I've got part C which is where I'm stuck

OK so far. Now, the set of values of x that satisfies both inequalities is the overlap between the two solutions (i.e. the values of x that fall within both solutions). To help visualise this, it might help you to shade in both solutions on a number line. The overlap should then be apparent.
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Beechey23
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Original post by old_engineer
OK so far. Now, the set of values of x that satisfies both inequalities is the overlap between the two solutions (i.e. the values of x that fall within both solutions). To help visualise this, it might help you to shade in both solutions on a number line. The overlap should then be apparent.


So would the answer be
1/4<x<1/2 and x>3
Original post by Beechey23
So would the answer be
1/4<x<1/2 and x>3


Yes, though its 'or' instead of 'and'

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