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  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#1 2019-10-27 17:53:31

666 bro
Member
From: Flatland
Registered: 2019-04-26
Posts: 706

Linear inequalities

When would the inequality signs gets reversed?


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#2 2019-10-27 18:38:44

Monox D. I-Fly
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From: Indonesia
Registered: 2015-12-02
Posts: 2,000

Re: Linear inequalities

When both sides is multiplied or divided by a negative number.


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#3 2019-10-27 21:06:31

Bob
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Registered: 2010-06-20
Posts: 10,053

Re: Linear inequalities

Rules in maths are designed to make maths useful in practical situations.

If you owe money then it's easy to understand why $3 owed is worse than $2 owed, so mathematicians have decided to use < in the sense of 'further to the left' on a number line.  Thus -3 < -2

It's defined that way for the convenience of any situation where 'better' means further to the right.  Another example would be with temperatures.  -3 is colder than -2 so again -3 < -2 makes sense.

If you have two positive points on a number line, A and B with A to the left of B; then A < B

But when you multiply or divide by a negative then -B is now to the left of -A so -A > -B

This doesn't happen if you just add something or subtract something ( A + x < B + x) as the new numbers are still in the same left to right order.

Bob


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#4 2019-12-26 19:13:19

666 bro
Member
From: Flatland
Registered: 2019-04-26
Posts: 706

Re: Linear inequalities

In solving word problems related to inequalities why do we use this symbol "≥'' for  at least?


"An equation for me has no meaning, unless it expresses a thought of God"- Srinivasa ramanujan

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#5 2019-12-26 20:12:24

Jai Ganesh
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Registered: 2005-06-28
Posts: 45,966

Re: Linear inequalities

At least in math means the smallest possible number in a set or sequence for example can not or must not be less than the given number.

The “greater than or equal to” symbol

conveys the same relationship as saying “at least equal to”.

Example: x is at least 2 =

.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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