Eternity Async Tutoring

Eternity · December 17, 2025, 5:01am

1.) Got it right (almost got it wrong, but I double checked and caught a mistake, my work doesn’t show the mistake)

My Work

4 - ((3x + 1)/4) = x + (3x+14)/2

4 - 3x/4 - 1/4 = x + 3x/2 + 7

16 - 3x - 1 = 4x + 6x + 28

15 = 13x + 28

-13 = 13x

x = -1

4 - ((3(-1) + 1)/4) = -1 + (3(-1)+14)/2

4 - (-3 +1)/4 = -1 + (-3 + 14 ) / 2

4 + 1/2 = -1 + (11/2)

8/2 + 1/2 = -2/2 + 11/2

9/2 = 9/2

Solution

2.) Got it right.

My Work

x = x/6 + x/12 + x/7 + 5 + x/2 + 4

x - x/6 - x/12 - x/7 - x/2 = 9

12x - 2x - x - 12x/7 - 6x = 108

3x - 12x/7 = 108

21x - 12x = 108(7)

9x = 108 x 7

x = 12 x 7

x = 84

84 = 14 + 7 + 12 + 5 + 42 + 4

84 = 84

Solution

3.) Got it right.

My Work

1 + 3(1 + 3(1 + 3(1+x))) = 13

1 + 3(1 + 3(1 + 3 + 3x) = 13

1 + 3(1 + 12 + 9x) = 13

1 + 39 + 27x = 13

40 + 27x = 13

27x = -27

x = -1

1 + 3(1 + 3(1 + 3(1+ - 1))) = 13

1 + 3( 1+ 3(1)) = 13

1 + 3(4) = 13

1 + 12 = 13

13 = 13

Solution

4.) Got this right the second time. I double checked my work, but I didn’t check it directly(?) through the word question. If I had did that maybe I would’ve caught the fact that I wrote -10 as the set-up fee instead of -40.

My Work

s = shirts sold

p_s = profit from shirts

5s - 10 = p_s

p_m = profit from magazines

t = subscriptions sold

p_m = 4t

p_m = p_s

t = s

4t = 5s - 10

4s = 5s - 10

10 = s

s = 10

if they sold 10 subscriptions they made 40 bucks. if they sold 10 shirts they made 50 bucks - 10 bucks. Profits from shirts equals profits from subs.

Got it wrong. I read 40 as 10.

4t = 5s - 40

4s = 5s - 40

s = 40

if they sold 40 subs they made 160 bucks, if they sold 40 shirts they made 200 bucks - 40 bucks = 160 bucks. profits from shirts equal profit from subs

Solution

5.) Got it right.

My Work

t = tank full of water. it has some volume

1/6t + 130 = 3/5t

130 = 3/5t - 1/6t

130 = 18t/30 - 5t/30

130 = 13t/30

130(30) = 13t

t = 10 (30)

t = 300

so when the tank is 1/6(300) we add 130 to get 3/5(300) 50 + 130 = 180, and 300/5 = 60 * 3 = 180

Solution

Eternity · December 18, 2025, 5:34am

1.) Got it right the second time. Even after checking it through the problem I was a bit confused on whether Cedric was included in the invited people.

i = people who were invited

2i/3 + 6 = 5i/6

4i + 36 = 5i

i = 36

2/3 of those invited (36) equals 24. 24 + 6 - 30 30/36 = 5/6. I assume Cedric is not counted later on too.

Hmm I got it wrong. Maybe it did include Cedric?

2i/3 + 6 + 1 = 5i/6

2i/3 + 7 = 5i/6

4i + 42 = 5i

i = 42

2/3 of 42 (those invited) = 28 add the seven people (six plus cedric) you get 35/42 = 5/6

2.) Got it right.

5 - 4x > 17, whats the highest integer value of x for which 5 - 4x is greater than 17

-4x > 12

x < -3

x has to be less than -3, so it can be all the negative numbers lower than -3 such as -4, –5, etc. The one with greatest value would be -4.

5 - 4 (-4)

5 + 16 = 21 21> 17

also lets check -3

5 - 4(-3) = 5 + 12

17 > 17, false, doesn’t work.

3.) Got it right

looking at just one workday

one workdays costs are $500 + $15 x 8 hours worked a day x number workers

one workdays revenues(?) are 5 widgets x 8 hours x 3.10

we want revenues greater than cost

w = number of workers

5 widgets per hour x 8 hours x 3.10 x number of workers > $500 + 15 x 8 x number workers

5 widgets per hour x 8 hours x 3.10 x w > $500 + $15 x 8

x w

40 x 3.10 x w > $500 + $120w

$124w > $500 + $120w

$4w > 400

w > 100

So they need to hire a minimum of 101 workers.

You pay $500 + ($15 per hour x 8 hours x 101 workers) = $500 + $120 x 101

You earn 5 x 8 x 101 x 3.10 = 124 x 101 =

uhh 500 compared to 4 x 101 = 404, hmm.

$124w > $500 + $120w

4w > $500 (not 400 woops)

w > 125

You pay $500 + ($15 per hour x 8 hours x 125 workers) = $500 + $120 x 125

You earn 5 x 8 x 125 x 3.10 = 124 x 125

500 compared to 4 x 125 = 500

ah 126 ttttt

You pay $500 + ($15 per hour x 8 hours x 126 workers) = $500 + $120 x 126

You earn 5 x 8 x 125 x 3.10 = 124 x 126

500 compared to 4 x 126 = 504

4.) Got it right

5m - 3 > 8m + 21

-3m > 24

m < -8

-9?

5 (-8) -3 > 8 (-8) + 21

-40 - 3 > -64 + 21

-43 > -43

5 (-9) -3 > 8 (-9) + 21

-48 > -72 + 21

-48 > -51

yes

5.) Got it right

.7 - 1.555

0.700 - 1.555

? subtract 1.5 from .5 = .5 - 1.5 = -1or -( 1.5 - .5)

so -(1.555 - 0.700)

-.855?

Eternity · December 19, 2025, 5:15am

Got all right.

1.) Got it right

My Work

(x+1)/x = 1.02, find x + (x + 1)

x + 1 = 1.02x

1 = .02x

.02x = 1

x = 1/.02

x = 1/(2 x 10^-2)

x = 1/2 x 1/10^-2

x = .5 x 10^2

x = 50

so 50 + (50 + 1) equals = 101

the quotient of two consecutive numbers with the larger one on top 51/50 equals 1.02 50/50 = 1, 1/50 is the same as 2/100 which equals .02. 1 + .02 = 1.02

Solution

2.) Got it right

My Work

we are adding the largest number and the smallest number of the four

3.9 is the largest, .39 is the smallest

4.29

Solution

3.) Got it right

My Work

round x/(10x - 3 ) to the nearest whole where x = .30103

.30103/(10 (.30103) - 3

.30103/3.0103-3

0.30103/0.0103

just thinking i think its 30

3010.3 x 10^-4 / 103 x 10 ^ - 4

3010.3 / 103

100 x 29 = 2900 3 x 29 = 87

2987 is the closest i can get to 3010. so 29 prob works?

Solution

4.) Got it right

My Work

roundest these numbers to the nearest ten = 20 / 10 + 20 = 2 + 20 = 22

nearest whole = 15 / 15 + 18 = 19

22 - 19 = 3

Solution

5.) Got it right.

My Work

reciprocal of 2 is 1/2

reciprocal of 1.67 is 1/1.67 (because 1.67 times that would equal 1)

expressing it as a simplified fraction? like no decimals. i assume no decimals

so 100/167

167 is not divisible by 2, 3, 5, 7, 11, 13 therefore 167 is prime

subtract numerator from denominator?

subtract 100 from 167? so 167 - 100 = 67

Solution

Elliot · December 19, 2025, 5:16am

Don’t worry about that one. That problem is confusing.

Eternity · December 19, 2025, 5:46am

Decided to share some of my daily writing (after I go through book quotes I tend to just more or less journal, I didn’t share the journaling). The stuff in square brackets is the title of book the quote is from. I said I’d share these more often in the past. Might as well start now.

Abusive men are masters of excuse making. In this respect they are like substance abusers, who believe that everyone and everything except them is responsible for their actions. - [[Why Does He Do That?]]

Hmm. Right. Like an abuser may hit their wife for, idk, making the food a bit too salty (which can be debatable, because he probably just felt its too salty today because he wanted to hit her for whatever reason). The abuser puts it on them for ruining their food after they’ve had such a long day.
Right. If they even think what they are doing is wrong, they are only doing this wrong action because they “have to”.

You’re never going to achieve your true potential if you’re hooked by what other people think. In fact, you could change your life overnight if you simply abandoned the notion that other people’s opinions matter. Life goes on, opinion heavy or opinion light. - [[Unfuk Yourself]]

I wonder how much he means this. I forgot about this book and its a self-help book I want to revisit.
I wonder how much we’re actually affected by what other people think? Probably a lot. How much could we improve if we ignored others though? Taking some standard complaints:
- Am I too lazy to workout because what others may think of me?
  - Hmm. Maybe if you feel like people will judge you and that is a subconscious issue you have that leads you to not feeling like working out
- Why am I too lazy to do dishes?
  - I may not care about having a clean house. I don’t think this is necessarily tied to others. Is it?
- I don’t want to eat healthy
  - What about others is affecting my decision on what to eat? if anything I think the stigma would lead to eating healthier (or developing an eating disorder), but most people don’t eat healthy

The goal of a manufacturing organization is to make money. - [[The Goal]]

Right. The goal is to make money. The goal is to be profitable(?). The goal isn’t necessarily maximizing profit.

(A male heart, Oz says, is in fact slightly different from a female heart. A heart surgeon can tell one from the other by looking at the ECG, because the intervals are slightly different. When you put a female heart into a man, it will continue to beat like a female heart. - [[Stiff]]

From Gemini:
- “No, female hearts in a male body (or generally) beat differently than male hearts==; female hearts are typically smaller, beat faster (higher BPM) to pump enough blood, have stronger contractions (contractility), but generate a lower overall blood volume (cardiac output) per minute compared to male hearts, due to intrinsic biological differences in size, structure, and function, not just body size. These differences, rooted in genetics and hormones, mean a female heart isn’t just a smaller male heart.”
  - Huh. Neat.