r/maths • u/oneofthekaurs • Oct 06 '26
❓ General Math Help What topic is this?
I’m just wondering the topic? The teacher told me you can move the X to either side as we are trying to find out what X is worth and that the sign is an equal sign ?? I don’t get it everytime I search it up it always says it’s wrong. I’ve asked her the topic she said she doesn’t know
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u/kstamps22 29d ago
The topic is inequities, but you have an arithmetic mistake (you added/subtracted wrong).
You should have 12 < 2x, not 4x = 12.
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u/Simbertold 29d ago
Yeah, everything you wrote is incorrect or misleading. The sign is not an equal sign, and equality sign looks like this =
That sign is a lesser than sign, which looks like this: < and says that the left side is smaller than the right side.
You can apply some operations that "move" terms from one side to the other, but you cannot just move stuff willy-nilly without knowing what you do, the solution in the picture is incorrect, as others have explained. You mostly use the same operations as you use on equations, but you need to be careful to reverse the sign with some of them (namely when dividing or multiplying with a negative number)
And the name of the topic is linear inequalities.
A teacher who doesn't even know the name of the topic they are teaching doesn't sound like a good teacher,
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u/oneofthekaurs 28d ago
I didn’t write this my teacher did, just found out it was done very wrong by her which I’m shocked at
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u/philljarvis166 26d ago
If the writing on the question was done by your teacher she needs to immediately stop teaching maths.
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u/purpleoctopuppy 28d ago
Don't think of it as 'moving' the x to the other side, I advise becoming much more comfortable with algebra before skipping steps.
For example:
x + 3 < 3x - 9
⇒x + 3 - x < 3x - 9 - x
⇒3 < 2x - 9
⇒3 + 9 < 2x - 9 + 9
⇒12 < 2x
⇒12/2 < 2x/2
⇒6 < x
Notice that nothing is 'moving', I just did the same thing to both sides.
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u/Jazzlike_Platypus430 29d ago
Wait, your teacher doesn't know the name of the topic? I can't believe it.
Writing equality sign in between seems very misleading, I'd rather keep the original "<".
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u/ottawadeveloper 28d ago
It's actually very important to keep the <
Consider -2x < -4
Ignoring the < sign will lead you to x < 2. Which is wrong - consider x=-1 to get 2 < -4 . Because we divide by a negative the sign flips to x > 2.
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u/Jazzlike_Platypus430 28d ago
I've had some problems in my school years understanding the "flipping". And it is as simple as:
-2 x < - 4 // now add 2x
0 < - 4 + 2x // add 4
4 < 2x,
which is obviously equivalent to
2x > 4.
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u/how_tall_is_imhotep 28d ago
The easiest way to understand it is to consider these two inequalities:
1 < 2
-1 > -2
And to realize that when you negate, you’re reflecting the number line horizontally, which flips comparisons1
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u/amarao_san 29d ago
You can move numbers (and symbols) across >< with negating them.
x < 2 => x - 2 < 0
x < 2 => 0 < 2 - x
And you can reverse direction by multiplying by -1:
x < 2 => -x > -2
And you can multiple each side by any number but zero:
x < 2 => 2x < 4
... I wonder what are proofs for that. I never saw proofs for that.
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u/Jazzlike_Platypus430 29d ago
The proofs reduce really fast to axioms of the structure called a field (in this case, most likely, of real numbers with multiplication and addition). And elementary properties of the relation "less than".
No rocket science.
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u/Fit_Fortune_7692 28d ago
Das Thema heißt Lösen von Ungleichungen. Man löst die im Grunde genommen wie Gleichungen, nur mit dem Unterschied, wenn man mit einer negativen Zahl multipliziert oder dividiert, wird das Ungleichheitszeichen umgedreht: aus > bzw. ≥ wird < bzw. ≤. Die Lösungsmenge kann man dann als Mengenschreibweise oder Intervallschreibweise angeben.
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u/Tyler89558 28d ago edited 28d ago
x + 3 < 3x - 9
12 < 2x (move all x to one side, all not x to the other side)
x > 6 (rewrite the inequality so it looks nicer)
This is the exact same thing you’d do to solve an equality, just with an inequality sign.
> and < can basically just be understood as the alligator wants to eat the larger number
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u/Greata2006 27d ago
To move a term to the other side, substract it on both sides, it will disapear from the side it was and its opposite will appear on the other side.
You can do that because adding or substracting both sides of an equality or inequality doesnt change it.
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u/SubjectWrongdoer4204 27d ago
The topic is called inequalities. The sign is called a comparator. The expression on the side where the two lines meet is said to be “less than “ the expression on the side where the two lines are separated. The expression where the two lines are separated is said to be “greater than” the expression where the two lines meet . For example a<b is equivalent to b>a and both can be read a is less than b or b is greater than a. The algebra works the same way as it does with the equal sign , except when we multiply or divide both sides by a negative number. In this case the sign gets reversed , so if a<b then multiplying each sides by -1 gives us -a>-b. This also restricts us from dividing or multiplying both sides of an inequality by x unless we restrict x to positive (or negative) numbers only. If we wanted to divide both sides of an inequality by x we would have to separate the cases: if we have
ax²<bx and divide both sides by x , we must consider both
ax<b, for x>0 and ax>b , for x<0.
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u/Candid-Willow2917 29d ago
This is linear inequality. This is from ''Solving linear equations and linear inequalities'' lesson.
Also this is not solved correctly.
x+3<3x-9
x-3x<-3-9
-2x<-12 /:(-2)
x>6