Wikipedia:Reference desk/Archives/Mathematics/2015 March 5

= March 5 =

Need help solving a seemingly simple equation
The equation is:

$$-2[x+5(1-x)]=3x$$

I'm stuck at the part:

$$-2[x+5-5x]=3x$$

I seem to be stuck because I don't know what to do with the single x. The equation's answer should be 2 btw... — Preceding unsigned comment added by 79.176.3.178 (talk) 03:47, 5 March 2015 (UTC)


 * Reorder the contents of the brackets: [5+x-5x] = [5-4x]. StuRat (talk) 03:49, 5 March 2015 (UTC)


 * $$-2x - 10 + 10x = 3x$$ Expand LHS
 * $$-2x +10x - 3x = 10$$ Collect x terms on LHS, constant terms on right
 * $$5x = 10$$ Add up terms on LHS
 * $$x = 2$$ Divide through by 5
 * GoldenRing (talk) 05:01, 5 March 2015 (UTC)


 * $$-2[x+5-5x]=3x$$


 * Rewrite as


 * $$-2[+ 1x +5 -5x]=3x$$
 * $$-2[+5+1x-5x]=3x$$
 * $$-2[+5-4x]=3x$$
 * $$-10 +8x=3x$$
 * $$-10 +8x -8x=3x -8x$$
 * $$-10 =-5x$$
 * $$-1 * -10 =-1 * -5x$$
 * $$10 = 5x$$
 * $$2 = x$$

175.45.116.65 (talk) 05:28, 5 March 2015 (UTC)

Everything is math
If everything is math, do mathematicians believe that biologist, literature critics, and such, know something about math? — Preceding unsigned comment added by Llaanngg (talk • contribs) 19:18, 5 March 2015 (UTC)

Wrong. Maths are a collection of (correct and very useful) ideas. Physical things are not ideas. And what maths is not about, maths is NOT about the truth. Maths is about consistency (within it's subject matter domain).

At least science can make the claim that it is the study of "things" found in the "real world". But maths can not make such a claim as it is the study of patterns and relationships of other "ideas". Whether these other ideas are the true state of reality, for example "Euclidean geometry" or "Non-Euclidean geometry", are not decided by maths. 175.45.116.65 (talk) 22:49, 5 March 2015 (UTC)


 * The paradigm of ideas vs. things demonstrates, but does not prove, that "everything is math" is wrong however. This is because typically, within scientific realism, ideas and physical things are usually kept separate, but because science admits fallibilism (the idea that we as a group are often all too wrong) such a scientific mind-body dichotomy isn't necessarily real and, in fact, the idea that everything is math is considered, for instance see the Mathematical universe hypothesis. Of course, regardless of whether everything is math, most everyone knows something about math. -Modocc (talk) 01:17, 6 March 2015 (UTC)

At the foundational level, you could say that everything is math: for example, a set implies inclusion/exclusion, so in a (very general) sense, any categorization of a subject domain can be considered mathematical. Going a bit further, any type of ordering is mathematical, so analyzing literature by its historical context requires math. However, both membership and order are such general concepts that this reasoning tells us almost nothing. You can get more traction by looking at how strict a subject's conceptual ontology is: for example, economics is fairly strict, while literary theory is very loose (sometimes to the extent that meaning is lost). OldTimeNESter (talk) 14:39, 6 March 2015 (UTC)