The inequality sign is not on any keyboard that I know of, but it sometimes can be found in special characters lists on word processing programs. On a manual typewriter, it can be made by overstriking an "=" with "/", if both are available.
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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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Yes you do, you also flip the inequality sign if you multiply by a negative # The > and < signs are strictly the "Greater than" and "Less than" signs. The inequality sign is an = with a / stroke through it. If you divide an inequality by -1 it remains an inequality.