How to write condition in math?

Question

How do I have to write condition in math?

For example,

Solve, $|x + 1| + |x - 1| \leq 2$

if x < -1
   -x - 1 - x + 1 <= 2
   -2x <= 2
   x >= -1
No solution
if -1 <= x < 1
   x + 1 - x + 1 <= 2
   2 <= 2
   Infinitely many solutions
-1 <= x < 1
if x >= 1
   x + 1 + x - 1 <= 2
   2x <= 2
   x <= 1
x = 1
So, -1 <= x <= 1

Can I write like this?

@Gary yes, but I am worried about my writing style because it looks a little weird. I saw some teacher using i) x < - 1 ii) -1 <= x < 1 would it be better to write like this? — doraemon1, May 13 '22 at 11:28
Where did $0$ come from? Btw, “how to write condition in math” is not an answerable question. I get what you’re saying, and your working is correct - except for the random introduction of $0$. You want to write: the solution is the set $[-1,1]$. — FShrike, May 13 '22 at 11:29
Perhaps you're confusing how to find the solution, versus how to present the solution once it's found. Did you ask this question to that teacher? — Joe, May 13 '22 at 11:39
@Joe umm no. My teacher writes like i), ii) but I don't like that. I may be a little stubborn — doraemon1, May 13 '22 at 11:43
It's just not clear to me if you are asking how to write the solution, or how to write your work leading up to the solution. The solution doesn't have cases. It's a set. The algebra to find the solution would typically be done in cases (on different intervals), to eliminate the absolute values. — Joe, May 13 '22 at 11:57
@Joe I'm asking about how to write work leading up to the solution — doraemon1, May 13 '22 at 12:05
Shouldn't the second line from the last be "x=1" instead of "x<=1" ? While it's optional to write "i)", "ii)", etc., and since you prefer not to enumerate the cases, I suggest at least utilising proper punctuation and capitalisation to separate your cases: "If....; if....;if... . Thus, ... ." — ryang, May 13 '22 at 12:48

miracle173 · Accepted Answer · 2022-05-13T15:03:54.357

if x < -1
   -x - 1 - x + 1 <= 2
   -2x <= 2
   x >= 1 ==> That is wrong, correct is x>=-1

No solution

Why not

if $x<-1$ then $$\begin{eqnarray}-x - 1 - x + 1 &\le& 2 \\ -2x &\le &2\\ x &\ge &-1 \end{eqnarray} $$ No solution!
(you have to append two blanks to the previous line to get this line break)
if $-1 \le x < 1$ then $$\begin{eqnarray} x + 1 - x + 1 \le 2 \\ 2 \le 2 \end{eqnarray} $$ so $-1 \le x \lt 1$

How to write condition in math?

1 Answers1