If guess you mean when doing algebra you have something like:
-x > 5
and you change it to
x < -5
when with an equals sign it makes no difference.
What you need to consider is what you are actually doing when you change the sign of an expression:
You are actually adding the same amount to both sides of the inequality:
-x > 5
→ -x + x > 5 + x
→ 0 > 5 + x
→ 0 > x + 5
Or subtracting the same amount from both sides:
→ 0 - 5 > x + 5 - 5
→ -5 > x
This is read (left to right) as: "-5 is greater than x"
Now if -5 is greater than x, then x must be less than -5, which would be written as: x < -5
The overall effect is to make it look like both sides have been multiplied by -1.
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It is only our convention for reading left to right that makes the '>' symbol to be known as "greater than", and the '>' symbol to be known as "less than":
They can, however, be read right to left, but KEEPING the expression at the wider end as the greater one:
Chat with our AI personalities
No. Only when you divide by a negative.
inequality sign
Yes, when the inequality has a less that or equal to sign, or a greater than sign or equal to sign, then the equal sign can be replaced and get a solution that is common to both the equation and the inequality. There can also be other solutions to the inequality, where as the solution for the equation will be a valid one.
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