Heartfelt Diary - Ch. 2 - How Can a Pretty Lady Who Loves Cats Have Bad Intentions?

[MangaDex]

 

[JusrKora]

Go lesbians go!

 

[yurri-homare]

can someone help me with my math hw

is that absolute value? i can barely remember how to solve those inequalities.
also thanks for the yuri, i love zhan chuyi and i want more of chang dan! everyone is drawn so gorgeously...

 

[Yuri_Enjoyer_Deluxe]

A catfight? Yes please...

Wait not the actual cats fighting, shi-

 

[JusrKora]

is that absolute value?

yes

i can barely remember how to solve those inequalities.

too bad help me

also thanks for the yuri,

np. ofc!

everyone is drawn so gorgeously...

so real omg. art is like beaiutiful

 

[FionaWitch]

https://imgur.com/a/sNDx7Y1

Chuyi is not gay..

 

[JusrKora]

https://imgur.com/a/sNDx7Y1

Chuyi is not gay..

yep thats right chuyi is NOT gay! (shes straight btw)

 

[GottagofastSonic]

Progress is being made! I repeat, progress is being made! Thanks for the chapter, JusrKora! As for your homework, inequalities were always a pain.

It's useful to think of k as a number of steps in the number line. Just remember that |x|<k for a positive number k (for negative numbers, this statement can never hold true). This is because logically, if you think of distance as "steps" away from 0, then it's saying that the distance of x from 0 must be less than k, so it needs to be less than k "steps" to the right (i.e. in the positive direction) and k "steps" to the left (i.e. in the negative direction, implying that x>-k and x<k).

Similarly, |x|>k for a positive number k (for negative k, it's always true since the absolute value function is strictly positive) implies that x>k or -x < -k (since x needs to be greater than k steps away from 0, meaning it either needs to be more than k steps to the left (negative direction) or more than k steps to the right (positive direction).

Though, it's much easier to see why these rules exist if you just test out a few values. Like, if given the question |x-1|<5, I'd list out what values |x-1| can equal (which are numbers between -5 and 5, since any number in that range will be closer to 0 compared to 5) and then you can create the inequality (-5<x-1<5) and solve.

 

[yurri-homare]

too bad help me

take my words with much salt, i looked it up but i'm not confident in my teaching or formatting. if you end up confused, i'm sorry (_ _

1. you have to isolate the absolute value expression by cancelling out the extra numbers. for example, (2|x+7|+8≤19) i bolded what needs to be isolated from the expression and italicized where it should go. (2|x+7|+8-8≤19-8) remember, multiplication/division after addition/subtracting. (2|x+7|≤11) -> (2|x+7|/2≤11/2)

2. check if the other side of the absolute value expression is negative or positive. if its positive, move onto step 3. if its negative, check the inequality sign. when it's < (lesser than), there is no solution since no positive is lesser than a negative. when its > (greater than), the solution is all real numbers since all positives are greater than negatives. absolute value refers to both the negative and the positive, so you have to consider that in this step.

3. when the inequality sign is < (lesser than) or ≤ (equal to or lesser than), write the absolute value inequality as a 3-part compound inequality. (|x+7|≤5.5 -> 5.5≤x+7≤5.5) when the inequality sign is > (greater than) or ≥ (equal to or greater than), write an "or" compound inequality (|x+7|≥5.5 -> x+7≥5.5 or x+7≤-5.5)

4. you just continue cancelling out everything in the middle until only x remains standing (-5.5-7≤x+7-7≤5.5-7 -> -12.5≤x≤-2.5)

boom, your answer (hopefully).

anything beyond this you'll just have to get help elsewhere because i am eepy. good luck on your homework, soldier!

 

[ThatSoulsGirl]

So far the cat’s who’s really making me wanna read this

 

[JusrKora]

take my words with much salt, i looked it up but i'm not confident in my teaching or formatting. if you end up confused, i'm sorry (_ _

1. you have to isolate the absolute value expression by cancelling out the extra numbers. for example, (2|x+7|+8≤19) i bolded what needs to be isolated from the expression and italicized where it should go. (2|x+7|+8-8≤19-8) remember, multiplication/division after addition/subtracting. (2|x+7|≤11) -> (2|x+7|/2≤11/2)

2. check if the other side of the absolute value expression is negative or positive. if its positive, move onto step 3. if its negative, check the inequality sign. when it's < (lesser than), there is no solution since no positive is lesser than a negative. when its > (greater than), the solution is all real numbers since all positives are greater than negatives. absolute value refers to both the negative and the positive, so you have to consider that in this step.

3. when the inequality sign is < (lesser than) or ≤ (equal to or lesser than), write the absolute value inequality as a 3-part compound inequality. (|x+7|≤5.5 -> 5.5≤x+7≤5.5) when the inequality sign is > (greater than) or ≥ (equal to or greater than), write an "or" compound inequality (|x+7|≥5.5 -> x+7≥5.5 or x+7≤-5.5)

4. you just continue cancelling out everything in the middle until only x remains standing (-5.5-7≤x+7-7≤5.5-7 -> -12.5≤x≤-2.5)

boom, your answer (hopefully).

anything beyond this you'll just have to get help elsewhere because i am eepy. good luck on your homework, soldier!

Progress is being made! I repeat, progress is being made! Thanks for the chapter, JusrKora! As for your homework, inequalities were always a pain.

It's useful to think of k as a number of steps in the number line. Just remember that |x|<k for a positive number k (for negative numbers, this statement can never hold true). This is because logically, if you think of distance as "steps" away from 0, then it's saying that the distance of x from 0 must be less than k, so it needs to be less than k "steps" to the right (i.e. in the positive direction) and k "steps" to the left (i.e. in the negative direction, implying that x>-k and x<k).

Similarly, |x|>k for a positive number k (for negative k, it's always true since the absolute value function is strictly positive) implies that x>k or -x < -k (since x needs to be greater than k steps away from 0, meaning it either needs to be more than k steps to the left (negative direction) or more than k steps to the right (positive direction).

Though, it's much easier to see why these rules exist if you just test out a few values. Like, if given the question |x-1|<5, I'd list out what values |x-1| can equal (which are numbers between -5 and 5, since any number in that range will be closer to 0 compared to 5) and then you can create the inequality (-5<x-1<5) and solve.

Thank youguys sm omg 😭🫶🏻
I didnt think anyone would actually help 😭

 

[Rayss]

take my words with much salt, i looked it up but i'm not confident in my teaching or formatting. if you end up confused, i'm sorry (_ _

1. you have to isolate the absolute value expression by cancelling out the extra numbers. for example, (2|x+7|+8≤19) i bolded what needs to be isolated from the expression and italicized where it should go. (2|x+7|+8-8≤19-8) remember, multiplication/division after addition/subtracting. (2|x+7|≤11) -> (2|x+7|/2≤11/2)

2. check if the other side of the absolute value expression is negative or positive. if its positive, move onto step 3. if its negative, check the inequality sign. when it's < (lesser than), there is no solution since no positive is lesser than a negative. when its > (greater than), the solution is all real numbers since all positives are greater than negatives. absolute value refers to both the negative and the positive, so you have to consider that in this step.

3. when the inequality sign is < (lesser than) or ≤ (equal to or lesser than), write the absolute value inequality as a 3-part compound inequality. (|x+7|≤5.5 -> 5.5≤x+7≤5.5) when the inequality sign is > (greater than) or ≥ (equal to or greater than), write an "or" compound inequality (|x+7|≥5.5 -> x+7≥5.5 or x+7≤-5.5)

4. you just continue cancelling out everything in the middle until only x remains standing (-5.5-7≤x+7-7≤5.5-7 -> -12.5≤x≤-2.5)

boom, your answer (hopefully).

anything beyond this you'll just have to get help elsewhere because i am eepy. good luck on your homework, soldier!

dang it, u god or somethin?

@JusrKora and the team, thx for the chap! i love it

 

[JusrKora]

dang it, u god or somethin?

Def a god 😭

@JusrKora and the team, thx for the chap! i love it

Np np! Glad you love it 🫶🏻

 

[Ne0_Moon]

The comment section under a yuri manhua (of all places) coming together to help the TL with their math hw has gotta be one of the most wholesome things ive seen down here

 

[yurri-homare]

Thank youguys sm omg 😭🫶🏻
I didnt think anyone would actually help 😭

dang it, u god or somethin?

ahaha i appreciate the compliments! @JusrKora i hope you understand absolute value a little more now!

 

[vixawi1793]

thanks for the TL!

laughing at chuyi for asking her robo assistant to open the door without even knowing who it is. girl, where is your sense of danger 😅