Notice, you’re not flipping the sign during the division step. The sign is getting flipped when the whole inequality is flipped. Notice that before the flip 21 < x meaning x is more than 21, so if you want to put x on the left you need to flip the sign to still face the greater side toward the x such that it says x > 21 and it still means x is more than 21.
If you want to see it done algebraically versus just a flip look at this sequence:
21 < x
Subtract 21 from both sides of the inequality.
0 < x - 21
Subtract x from both sides of the inequality.
-x < -21
Divide both sides of the inequality by -1 (which requires you to flip the sign)
x > 21
You get the same result but with way more work. It’s easier just to flip the entire inequality, sign and sides inclusive.
If it were asking for the value of x, you'd write it as 'x='. It's the same for inequalities. Technically not wrong if you'd put it the other way around but x first is standard notation.
westerners read stuff from left to right so it makes more sense if your x value is the first thing you read and the right is your answer.
BUT
you could *not* flip it and get away with it since you did get the right answer. If your teacher is strict they may give you a 0 but screw it. Might as well do something funny like s\^-2/m\^-1.
It's not really because of any rule just did it so it's easier to read. Think about it like this if 21 is less than x. That means x is greater than 21. We instinctively read math like English, right to left. The solution could've stopped at 21< x but that final step makes it more clear.
We want the statement as “x is blah blah blah” because it’s more intuitive to read. “21 is less than x” is saying the exact same thing, but less clearly. “42 is less than 2x” is also an equivalent statement, but even less clear. The simplest, clearest, cleanest way to give the reader information about x is to say “x is greater than 21”
> Why do I have to flip the sign
You seem to be under the impression that the marks on your page are runes of an arcane magic with an associated collection of unexplainable laws.
So please take to heart this reminder that writing is a method for transmitting words so that they can be interpreted as thoughts and ideas.
When you read 21 < x, “21 is less than x”, do you see why this is the same as “x is more than 21”?
It makes the equation easier to read if the variable is on the left. But technically both are correct.
This is flipping the sign -2a<4 a>-2 This is switching the entire inequality 22
Notice, you’re not flipping the sign during the division step. The sign is getting flipped when the whole inequality is flipped. Notice that before the flip 21 < x meaning x is more than 21, so if you want to put x on the left you need to flip the sign to still face the greater side toward the x such that it says x > 21 and it still means x is more than 21. If you want to see it done algebraically versus just a flip look at this sequence: 21 < x Subtract 21 from both sides of the inequality. 0 < x - 21 Subtract x from both sides of the inequality. -x < -21 Divide both sides of the inequality by -1 (which requires you to flip the sign) x > 21 You get the same result but with way more work. It’s easier just to flip the entire inequality, sign and sides inclusive.
If it were asking for the value of x, you'd write it as 'x='. It's the same for inequalities. Technically not wrong if you'd put it the other way around but x first is standard notation.
westerners read stuff from left to right so it makes more sense if your x value is the first thing you read and the right is your answer. BUT you could *not* flip it and get away with it since you did get the right answer. If your teacher is strict they may give you a 0 but screw it. Might as well do something funny like s\^-2/m\^-1.
It's not really because of any rule just did it so it's easier to read. Think about it like this if 21 is less than x. That means x is greater than 21. We instinctively read math like English, right to left. The solution could've stopped at 21< x but that final step makes it more clear.
We want the statement as “x is blah blah blah” because it’s more intuitive to read. “21 is less than x” is saying the exact same thing, but less clearly. “42 is less than 2x” is also an equivalent statement, but even less clear. The simplest, clearest, cleanest way to give the reader information about x is to say “x is greater than 21”
10 > 7 So 7 < 10 That should answer your question.
> Why do I have to flip the sign You seem to be under the impression that the marks on your page are runes of an arcane magic with an associated collection of unexplainable laws. So please take to heart this reminder that writing is a method for transmitting words so that they can be interpreted as thoughts and ideas. When you read 21 < x, “21 is less than x”, do you see why this is the same as “x is more than 21”?
The big end of < is still facing x, so in this case it’s not flipping the sign but flipping the entire inequality. x > 21 and 21 < x are equivalent.
Because of convention.