Any Mathematicians out there?

[SpotEnemyBoats]

I have a huge Math final tomorrow, and I have one question. In an algebriac solve for X equation, whats the difference between greater/less than and greater/less than or equal to?

Like a problem like:

-3(2y-7) < -9y+9

which Y becomes: -4

What symbol it flips or changes to to represent the variable? How does it become said symbol?

 

[Sheepo]

I understand the problem but I have no idea what you're asking.

 

[SpotEnemyBoats]

How does the '<' change on what part of the equation? And whats the difference between greater than, and greater than or equal to? That's what I am asking.

 

[joule]

iirc, the symbol flips only when dividing by a negative.

 

[VirusType2]

lets say x=3

greater than is x > 1

greater than or equal to is x >= 3

 

[Sheepo]

Dividing or multiplying by a negative flips the sign. 'Greater than' and 'greater than or equal to' are all in the names.

X is greater than 10 means any number higher than 10 (10.0001, 12, etc.) could be equal to X.

X is greater than or equal to 10 means that 10 itself and any number higher than it (10, 10.0001, 12, etc.) could equal X.

 

[Maestro]

You must be a freshman in high school or something.

OK...

GREATER THAN OR EQUAL TO: means that it must be greater than the value of Y, or equal to the value of Y, where Y is the variable you solved for.

GREATER THAN: means that it must be greater than the value of Y.

I believe changing the negative or positive sign of the variable (Y) is on will modify which side is greater or lesser, but I don't quite remember. I don't do many < or > equations anymore.

As to that specific problem, see if you follow me.

-3(2y-7) < -9y+9

(2y-7) < 3y-3

-7 < y-3

-4 < y

Since you did not change the negative or positive sign of the Y then it is still "Negative 4 is less than Y."

Ya dig?

 

[Kinslayer]

What Maestro said, but he messed up.

The sign flips when you multiply or divide by a negative.

So, solving for y it would be:

-3(2y-7) < -9y+9

(2y-7) > 3y-3

-y - 7 > -3

- y > 4

y < -4

You can check the answer by substituting a value y < -4, and then seeing if the inequality holds up. In Maestro's, you can substitute -3, and the inequality comes out as 39<36, which is not true and thus his solution is incorrect.

 

[SpotEnemyBoats]

Yeah, I know that the '<' and the '>' sign flips when there is a negative in the numerator when dividing. What makes a particular sign flip to a '>=' or a '<=' sign? That's what I am confused about. *sees head scratching amongst you*

BTW I am in College.

 

[joule]

The same rule would apply I would assume.

 

[mindless_moder]

Simply check what values of y will satisfy the inequality.

 

[Qonfused]

erhteyj nevermind

 

[Maestro]

What Maestro said, but he messed up.

The sign flips when you multiply or divide by a negative.

So, solving for y it would be:

-3(2y-7) < -9y+9

(2y-7) > 3y-3

-y - 7 > -3

- y > 4

y < -4

You can check the answer by substituting a value y < -4, and then seeing if the inequality holds up. In Maestro's, you can substitute -3, and the inequality comes out as 39<36, which is not true and thus his solution is incorrect.

Shit.

I haven't done inequalities in forever, sorry.

 

[Danimal]

erhteyj nevermind

Same here.

I throw out words and wave my arms but it ends up being a jumble on confusion.

 

[dfc05]

Yeah, I know that the '<' and the '>' sign flips when there is a negative in the numerator when dividing. What makes a particular sign flip to a '>=' or a '<=' sign? That's what I am confused about. *sees head scratching amongst you*

BTW I am in College.

If your original problem statement is < or >, you keep it that way without the equal sign. If it's <= or >= you keep the equal sign.

When you solve for an answer for the variable (e.g. saying y is -4 in your original example), you're essentially solving for the number that y would be to make the two sides of the equations equal, e.g. at y=-4, then -3(2y-7) EQUALS -9y+9. So if your problem asks for something < or > but NOT equal, then y needs to be < or > what you solved for but cannot be equal to the number you solved for. If it asks for something that CAN be equal (e.g. <= or >=), then your solution for y is acceptable and so you keep it as <= or >=.

I know that was written in a totally confusing way, so in short, don't add or remove the equal sign when you work the problem. Leave it the way it already is.

 

[theotherguy]

I have a huge Math final tomorrow, and I have one question. In an algebriac solve for X equation, whats the difference between greater/less than and greater/less than or equal to?

People have already answered the question in this thread, but I want to expound on this to maybe help you understand how algebraic equations are supposed to work in general.

Whenever you have an algebraic equation, it defines a set of values. That is, it is the set of all values such that the equation is true.

For some equations, there is only one value such that the equation is true.

Let's look at this equation:

3x = 4

What this equation defines is all values x, such that 3x = 4.

Using algebra, we can deduce that this equation is equivalent to

x = 4/3

because they define the same set. It turns out that there is only one possible value of x such that the equation "3x=4" holds true, where x = 4/3.

For other equations, multiple values can make the equation true.

Take for instance:

(3-x)*(2-x) = 0

In this instance, there are two values that make the equation true

x=3

and

x=2

So the set of values that the equation "(3-x)(2-x)=0" defines is the set {3, 2}.


Now let's talk about inequalities. Inequalities define the boundaries of a set.

The equation:

x<4

defines the set of all values x, such that x is less than 4. ie {3,2,1,0,-1,-2,...}

You can imagine the equation as sort of slicing up the numberline right at x=4, and everything to the left of the slice is included in the set, and everything to the right of the slice is not, like this:

-5, -4, -3, -2, -1, 0, 1, 2, 3, |*slice*|4, 5, 6

The difference between less than, greater than, less than or equals to, and greater than or equals to is that these two: (<=, >=) define an inclusive boundary, while these two (<,>), provide a non-inclusive boundary. What is the difference between inclusive and non-inclusive boundaries?

Let's look at the equation:

x<=4

This defines he set of all values x, such that x is less than or equal to 4. ie {4,3,2,1,0,-1,-2,...}

This slices up the number line, just as before, but it also includes the numbers along the boundary. Whereas before, with "x<4" it excluded them. Like this:

-5, -4, -3, -2, -1, 0, 1, 2, 3,4|*slice*|, 5, 6

This concept may seem tedious now, but it will become very important when you start to reason about inequalities, and particularly about inequalities with multiple variables, like in the XY plane, or in 3D space.

So, keep in mind that when you're looking at an inequality, you are attempting to define a set of numbers that make it true, not just finding a single number. How do you define a set? By reducing it to a simpler inequality that has the variable by itself on one side, and constants on the other.

For instance:

"3x<4"

implies that

"x<3/4"

And this is the simplest inequality we can find. It defines the set of all numbers x, such that x is less than 3/4. That means you can just write "x<3/4" as your answer, and you are finished, just as you could write "x=3/4" as before.

And in

3x<=4

we have that

x<=3/4

This is exactly the same as before, except it now defines a set of numbers less than 3/4, and also the number 3/4 itself.

What symbol it flips or changes to to represent the variable? How does it become said symbol?

When multiplying through by a negative value, you change the sign of both sides of the inequality. Let's look at an inequality with just constant values:

3<4

This is a true inequality. Just like with equations, we can do whatever we want to both sides of a true inequality, and it will still hold true. So let's multiply both sides of the inequality by -1.

We get:

-3<-4

But this is not true! You see, on the number line, less than or greater than is reversed for the negative numbers. The "bigger" a negative number is (the further away from zero) the less it becomes. Because of this, we have to flip the sign of the inequality every time we multiply or divide by a negative number,

giving

-3>-4

which is true.

You have to do the same thing every time, even when variables are involved.

This isn't the most rigorous of explainations, but I hope it was helpful.

 

[SpotEnemyBoats]

Yeah, I understand it. Also, I got a 84 on the final!

 

[DEATH eVADER]

I forgot how much I hate Calculus, but I need to study it if I want to attempt to do Electrical and Mechanical Engineering

 

[Barnz]

wait a second...








this isn't right...









OH MY GOD, JC! IT'S A BOMB!

 

[Maestro]

I forgot how much I hate Calculus, but I need to study it if I want to attempt to do Electrical and Mechanical Engineering

You will never use greater than/less than equations in practical applications. I love limit notation, it is so much more useful.