Quick Questions (1 Viewer)

[davidbarnes]

What does the 'O' in BODMAS stand for?

Can anyone help me with the following algebra qustions.

(x²)² - How do I expand when both are squared?

(x + 5)² + (1 - x)(1 + x)

(x - 3)(x² - 2x + 7)

(2x - 5)(3x² + x - 4)

Also is the answer to the below question x > -45 or x > -23 (ignore the dots)

2x + 11 > 3x - 1
--------- --------
...2................4

Thnakyou.

 

[SoulSearcher]

(x²)² = x^2*2 = x⁴, basic index laws.

The next three, just simply expand the brackets and simplify.

4x+22 > 3x-1
x > -23

 

[davidbarnes]

So for the last one, you cross multiply? How do you know which product goes on what side of the sign (>, etc).

 

[pLuvia]

You use test points if you are not sure, best points to use are 0 or any point in between the values you have found

 

[davidbarnes]

I have no idea at all what test points are. Teacher isn't the best, and I'm not very good at algebra, so have no idea what this is. So what are test points?

 

[pLuvia]

Just so you can determine what the signs could be, let's say for you question use the test point x=0, since x=0 does not satisfy the equation then the region of the inequality must not satisfy the point x=0 and so the answer is x>-23.

This method is just a check, but becomes very handy

 

[davidbarnes]

LOl, I still don't get it.

 

[pLuvia]

Ok let's use a simple example
Take
(x²-x-12)>0
(x-4)(x+3)>0

Now we know that the answer is x<-3 and x>4 but if we wanted to check this we could use a value in between these two values, let's say x=0 (since it's the easiest)
Now sub x=0 into (x-4)(x+3) and then you can see that it is not greater than 0

That is:
0+0-12
=-12

And -12 is not greater than 0 and so x=0 does not satisfy the equation therefore the numbers in between x=4 and x=-3 do not satisfy the inequality and so the signs are x>4 and x<-3 not -3<x<4

Hope that's clear enough.

It's not an important method, but it is very handy for checking answers

 

[Raginsheep]

For the last one, (2x+11) / 2 > (3x-1) /4, you can just multiply both sides by 4.

Cross multiplication also works but since your multiplying by constants, you don't need to test for anything. Just remember to switch the '>' or '<' sign around if theres a negative involved.

Actually, what's this testing of the points Pluvia? The above question involves linear inequalities only.

 

[pLuvia]

Dammit, ignore what I said, didn't read the question properly.

But still that method can be used for quadratics, cubics etc.

 

[adgala]

BODMAS = Brackets of Division Multiplication Addition Subtraction

 

[davidbarnes]

For the last one, (2x+11) / 2 > (3x-1) /4, you can just multiply both sides by 4.

Cross multiplication also works but since your multiplying by constants, you don't need to test for anything. Just remember to switch the '>' or '<' sign around if theres a negative involved.

Actually, what's this testing of the points Pluvia? The above question involves linear inequalities only.

Thats what I don't get. Would multiplying by 4, not cuase the left side to be unbalanced?

 

[davidbarnes]

BODMAS = Brackets of Division Multiplication Addition Subtraction

Thanks, I thought that was waht it was.

 

[davidbarnes]

Ok let's use a simple example
Take
(x²-x-12)>0
(x-4)(x+3)>0

Now we know that the answer is x<-3 and x>4 but if we wanted to check this we could use a value in between these two values, let's say x=0 (since it's the easiest)
Now sub x=0 into (x-4)(x+3) and then you can see that it is not greater than 0

That is:
0+0-12
=-12

And -12 is not greater than 0 and so x=0 does not satisfy the equation therefore the numbers in between x=4 and x=-3 do not satisfy the inequality and so the signs are x>4 and x<-3 not -3<x><4

Hope that's clear enough.

It's not an important method, but it is very handy for checking answers

Still don't get it lol.
</x>

 

[airie]

Just remember: when you multiply or divide both sides of an inequality by a positive number, the inequality still holds (and no, it will not "unbalance" the inequality, since you're carrying out the operation on bothsides). It is only when you multiply or divide both sides by a negative number that the inequality sign reverses.

Addition/subtraction of ANY number on both sides does not affect the inequality (ie. it still holds whether you add/subtract a positive OR a negative number).

In your example you're multiplying both sides by 4, a positive number, so the ineuqality still holds. Then just subtract 3x and subtract 22 on both sides to get x is greater than -23, as SoulSearcher has done above.

EDIT: And what pLuvia was talking about was just to sub a random value of x into the inequality and see if it holds. In your example, the result you get is x>-23, so it "splits" the domain of real numbers into two parts: one containing all numbers greater than -23, and one that is less than -23. (The one number that equals -23 is not in consideration as the inequality sign is a "strictly greater than" ) So in order to check if you've got the right range of values, just sub any value in that range into the inequality; if it holds, (and you know you've got the critical point -23, the one that "splits" the domain, right) then you know you've got the right one. pLuvia used 0 (as it often simplifies the arithmetic ), so LHS = 2*0 + 11 = 11, RHS = 3x - 1 = -1. And since 11>-1, x=0 satisfies the original inequality. Because 0 is in the range x > -23, you can convince yourself that your answer is right

 

[Raginsheep]

Thats what I don't get. Would multiplying by 4, not cuase the left side to be unbalanced?

Why would it do so?