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What role of operations that applies when you are solving an equation does not apply when your solving an inequality?"
You can add, subtract, multiply, or divide both sides of the equation or inequality by the same number. Don't multiply or divide by zero. In the case of an inequality, if you multiply or divide by a negative number, the sign of the inequality must be reversed. E.g., if you multiply both sides by -2, a "less-than" sign should be replaced by a "greater-than" sign.
You solve an inequality in exactly the same was as you solve an equation, by doing the same thing to both sides. The only difference is if you multiply/divide by a negative number, when you have to turn the inequality around.
This isn't an inequality, since there is no less-than, greater-than, less-than-or-equal, or greater-than-or-equal sign. However, solving inequalities is similar to solving equations; however, when you multiply by a negative number, you must change the direction of the inequality sign.
The main difference is that if you multiply both sides of an inequality by a negative number, you have to change the direction of the inequality sign - for example "greater than" would become "less than".