mathematics - Move a single match to make this expression true

Move a single match to make the following expression true:

So far I've found 6 valid solutions, can you find all 6? (or more!)

Edit: Lots of great, creative answers! All 6 I found are represented among the answers, plus quite a few more!

A few clarifications:

1. I changed "equation" to "expression" in the title and question, for the mathematically pedantic. This officially allows for inequalities.


2. The expression still has to logically evaluate to true or false in a boolean sense. So "8 + 4 - 4" wouldn't count, even though it might be treated as TRUE by most programming languages.


3. You're not limited to "perfectly-formed" LED-style numbers, although using a single vertical match as a "1" is kind of stretching it. But I'll allow it, if it gets us more good answers.

Answer

Here are the compiled expressions from the current answers. These are from Glorfindel's answer, Matt's answer, humn's comment, as well as the various other comments on other answers. I have also added alphabetic labels to identify the unique relations and the different expressions.

Expressions A through G are either equations and strict inequalities with one operator:

[A] 0 + 4 = 4
[B] 5 + 4 = 9
[C] 8 - 4 = 4
[D] 6 + 4 > 4
[E] 6 ≠ 4 - 4
[F] 5 + 4 ≠ 4
[G] 6 - 4 ≠ 4

If expressions can have multiple inequality operators, then you also get expressions H and I:

[H] 5 ≠ ­4 ­= ­4
[I] 6 > 4 = 4

In total, that's 9 unique relations listed above.

For some of the inequalities that contain ≠, you can rewrite the expression with a different inequality operator. Because these new expressions have similar structure, I indicate them with a * suffix.

If the + was changed into ≠, then the + can also be changed into a negated strict inequality (either ≮ or ≯). Or, if the = was changed into ≠, then the = can also be changed into a non-strict inequality (either ≥ or ≤).

[E*] 6 ≮ 4 - 4
[F*] 5 + 4 ≥ 4
[G*] 6 - 4 ≤ 4

[H*] 5 ≮ ­4 ­= ­4

This raises the total to 13 different expressions.

If you allow a single vertical match to count as the number 1, then there are more expressions that you can form, using the same rules as above:

[J] 614 ≠ 4
[J*] 614 ≥ 4
[K] 6 + 4 ≠ 11
[K*] 6 + 4 ≤ 11
[L] 6 + 11 ≠ 4

[L*] 6 + 11 ≥ 4

These additional expressions raise the total to 19.