maths p1-inequalities

[khizarr]

i'm having some problems regarding inequalities, nov02/11(iii) ,june03/11(iii), jue04/10(ii), nov06/10(i),
i would be very thankful if u go step by step for the first two questions. the main problem i'm having is the chenges to the sign when shifting the number to left side.

 

[kevin_ram19]

Hi,

Remember, the ≥ sign won't change for adding or subtracting number both sides. And same when multiplying/dividing both side using positive numbers, the sign won't change.

Sign changes/swaps only when you multiply or divide both sides with a negative numbers. Refer to the link below for more details.

http://www.s-cool.co.uk/alevel/maths/basic-algebra/inequalities.html

Solution for nov02/11(iii).

2x^2+8X-10 ≥ 14
2x^2+8X-24 ≥ 0
2(x^2+4X-12) ≥ 0
2 (x-2)(x+6) ≥ 0

Now you sketch a graph or number line.
I've used graph method. I've sketched a graph for plotted the roots 2 and -6.

Then, let 2(x-2)(x+6)=y,

2 (x-2)(x+6) ≥ 0
y ≥ 0

Now look for the region where the y ≥ 0 in the graph and shade it.

The x values which satisfies the inequalities are always lesser than -6 and more than 2. Hence,

x ≤ -6
X ≥ 2

After finding them, just try to check again whether they satisfy the inequalities or not by substituting back those values into the equation.

 

[Mohammad Aamer]

Ok..I'm gonna try to explain... {pls consider this sign '>/=' as greater than or equal to and vice versa }
since fx >/= 14

....factorise..you'll get this (x-2)(x+6)>/=0

I usually draw the inequality table here...theres another way though...i dunno that. this is the trickier part...
Consider that now you have 4 possibilities

1.x>/=2
2.x>/=-6
3.x</=2
4.x</=-6
Now draw the inequality table using these four values.

If you want me to explain the table you're most welcome just let me know...and one more thing.. an equality sign only reverses when you are multiplying or dividing both sides by minus.

 

[khizarr]

ohhhhhh thanks alot boys! thank youuuuuuuu aamer and kevin!!!
this has been troubling me since the last coupple of weeks! thanks!
kevin, that was amazing! aamer, yours was a bit tricky but was of great help to me!

 

[zahraahmed]

http://notezone.net/cambridgechem/chemi ... sis%5D.pdf can sum1 go in dix page 11 n do solve n gimme answers plzzzz i cant able to slove it n it might cum for exam help mee!!!!