Question 3d, why is the answer no value, when similar question have answers?

[thorny storm]

3d's answer is no value but 3f and 3g have answers that look like this, {x:x<= -2/3} U {x: x >=3/2} ???

[drowsy hatch]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations
4. Do not ping the mods, unless someone is breaking the rules.
5. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[cloud heron]

"no values" is not a set.
it shld b the empty set ∅

"x = 4" is an equation, but not a set.
"{x | x = 4} = {4}". "{4}" is a set (with one single element known as "singleton")

[thorny storm]

I still don't get it? 😕

[cloud heron]

have you ever tried solving the question?
if yes show us your work, so that we know where u r stuck

[thorny storm]

@cloud heron thanks btw

[vivid heart]

@thorny storm has given 1 rep to @cloud heron

[cloud heron]

u r welcome
it's true that no value from the set of real numbers ℝ can satisfy the system in question (3d), so the set of solutions is a set with no elements. This is known as the "empty set" in math.
https://en.wikipedia.org/wiki/Empty_set

the question is asking for the set of solution in set notation, but the model answer isn't in set notation.
that's why i'm commenting on that

the answer for (3e) is also not well-written cuz nowadays, when we write a set in the set-builder notation, we'll use a pair of curly braces {...} to wrap it up.

[thorny storm]

Oh rightt that makes sense but at the same time, I've never heard of the o with a slash symbol. And the e question, you're right it defo needs the { } curly brackets. Why is it empty set and not {x:x<7} U {x: x >8}?

[cloud heron]

let A and B be two sets
the set union of A and B "A ∪ B" is the set of elements that belong to A or B (or both)

image source: https://www.researchgate.net/publication/332453167/figure/fig1/AS:748486492450816@1555464494152/A-Venn-diagram-of-unions-and-intersections-for-two-sets-A-and-B-and-their-complements.png

"a ∈ {x : x < 7} U {x : x > 8}" means "a < 7 or a > 8"

but in case of simultaneous equations, each condition (represented by an equality/inequality in a line) has to be satisfied, so it should be the intersection of the all sets that correspond to the conditions

the given system

,,\begin{cases} f_1(x) &\le c_1 \ f_2(x) &\le c_2 \end{cases}

[dusk bay]

vin100

[cloud heron]

is actually a set union

,,{x \mid f_1(x) \le c_1} \cap {x \mid f_2(x) \le c_2 }

[dusk bay]

vin100

[cloud heron]

the statement "x < 7 AND x > 8" is false, so no values of x can satisfy this statement.

[thorny storm]

@deep arch

[deep arch]

Solve the inequalities.

[thorny storm]

I'm gonna have to go through this again

[deep arch]

15 - x < 2(11 - x)
15 - x < 22 - 2x
15 + x < 22
x < 7

5(3x - 1) > 12x + 19
15x - 5 > 12x + 19
3x - 5 > 19
3x > 24
x > 8

x < 7 AND x > 8 is impossible```

And that's officially the end of my patience, sorry. Should've spent less time asking permission and more time asking your questions.

[thorny storm]

I was overly polite my bad. But yh I should get straight to the point 🤣

[cloud heron]

OP has alr done it the calculations right
#1173919349346664520 message
so that's no need to repeat what he/she has alr known

[thorny storm]

OMG I was so perplexed but I did not even read the question properly, I didn't realise the and n or in the question. Hence I was so confused. Thank you so much!

[vivid heart]

@thorny storm has given 1 rep to @cloud heron

[deep arch]

Except that it is necessary because OP asked me to explain this to them and then said they would have to redo the work.

Seriously, read the context. It's not hard, I replied directly to it.

[thorny storm]

Also, thank you ask well!

https://tenor.com/view/cant-thankyou-enough-gif-25170543

Anyways, thank you to both! @cloud heron @deep arch

[vivid heart]

@thorny storm has given 1 rep to @deep arch @cloud heron

[thorny storm]

+close