Harder inequalities... (1 Viewer)

[KimmorleyKiller]

Ive a couple problems that would be great if someone could show the working out for me...

|5/2x-1| < 1

(2-x)(2x-1)(x+3) less than/equal to 0

2x+3/x-4 > 1

-3x^2+10x+8 less than/equal to 0

Cheers guys!

 

[kami]

I'm a bit rusty, but here you go...

|5/2x-1| < 1

2x - 1 <0 and 2x - 1 >5 [because dividing by 0 gives infinity, dividing by 5 gives 1, and anything in between will push it above 1]
∴ x< 1/2 and x >3

(2-x)(2x-1)(x+3) less than/equal to 0

to be equal to 0, x must be either 2, 1/2 or -3
a quick way to then find where it is less than 0 would then be to graph it but I'll just use some substitution here:

• when x = 1, y = 4 so between 2 and 1/2 is not less than 0
• when x = -1, y = -18 so when x is between 1/2 and -3, y is less than 0
• when x = 3, y = -30 so when x is greater than 2, y is less than 0
• when x = -5, y= 154 so when x is less than -3 it is not less than 0

∴ your answer is 1/2 ≥ x ≥ -3 and x ≥ 2

I might give the others a go later after I've done my uni hw

 

[pLuvia]

2x+3/x-4 > 1

x =/=4

2x+3 > x-4

x<-7 x>4

-3x^2+10x+8 < 0

3x²-10x-8>0

(3x+2)(x-4)>0

x<-2/3 x>4

Use test points if your not sure which way the sign goes usually use 0

 

[Mountain.Dew]

just a general tip...when you do have a factorised form, draw the actual curve of it on a number plane. then, the solution is for x-values where the curve is below the x-axis (for <= 0) or above x-axis (for >= 0). i find this much better than testing points.

 

[pLuvia]

But isn't this the same thing? if you just test the point in between the 2 numbers let's say and it doesn't fit the condition then the x/y values are outside i.e -a<x x>b and vice versa.

Your way is for the more visual person I guess

 

[Mountain.Dew]

But isn't this the same thing? if you just test the point in between the 2 numbers let's say and it doesn't fit the condition then the x/y values are outside i.e -a<x x="">b and vice versa.

Your way is for the more visual person I guess

yeah, i suppose so. either way is equally valid and effective. its all a matter of personal preference.
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[Riviet]

just a general tip...when you do have a factorised form, draw the actual curve of it on a number plane. then, the solution is for x-values where the curve is below the x-axis (for <= 0) or above x-axis (for >= 0). i find this much better than testing points.

I like to draw the curve in my head.

 

[Mountain.Dew]

I like to draw the curve in my head.

although it would be nice if u did draw the curve on the test paper so the marker actually knows how you got your final solution.

 

[KimmorleyKiller]

Cheers, thanks a lot for your help guys...*high five