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# Inequalities

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For example, (2x+3)(x-1)<0 is -3/2x<x<1 but how do you know it's one inequality and not -3/2<x and 1>x

And then (3x+1)(1-x)<0 why would it be two separate inequalities of x<-3 and x>1?

Also as a third example (3x-2)(2x-1)>or equal to 0 is x<or equal to 1/2 and x>or equal to 2/3
2. (Original post by Lucofthewoods)
For example, (2x+3)(x-1)<0 is -3/2x<x<1 but how do you know it's one inequality and not -3/2<x and 1>x

And then (3x+1)(1-x)<0 why would it be two separate inequalities of x<-3 and x>1?

Also as a third example (3x-2)(2x-1)>or equal to 0 is x<or equal to 1/2 and x>or equal to 2/3
It is very simple if you sketch a parabola with the corresponding roots, then just look for which domain the parabola satisfies the inequality. Do enough of these and you'll start recognising these without a sketch.
3. (Original post by Lucofthewoods)
For example, (2x+3)(x-1)<0 is -3/2x<x<1 but how do you know it's one inequality and not -3/2<x and 1>x

And then (3x+1)(1-x)<0 why would it be two separate inequalities of x<-3 and x>1?

Also as a third example (3x-2)(2x-1)>or equal to 0 is x<or equal to 1/2 and x>or equal to 2/3
For the first consider (2x+3)(x-1) = 0

We know that the solutions are x = -3/2 or x = 1 so draw a sketch of the graph.

Which part of the graph represents the inequality you want to solve?

I would always suggest drawing a sketch as it is then clear.

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Updated: October 10, 2016
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