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When would the inequality signs gets reversed?
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When both sides is multiplied or divided by a negative number.
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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.
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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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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 =
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