-
Yet this seems easy: you only need to apply the few rules (see "In Brief: Basic Inequalities") governing how operations (addition, multiplication and division) interact with inequalities. Yes, that's all… Easier said than done!
The hardest rule to apply is, of course, the one about multiplication: remember to reverse the direction of the inequality when multiplying by a negative number, and remember to consider both cases when the sign of the multiplier is unknown. Let's look at an example. Solve the inequality 3x + 1 ≤ 5 ‒ x.
Adding ‒1 to both sides gives 3x ≤ 5 ‒ x, and then, adding x, gives 4x ≤ 5. All this is possible because addition preserves inequalities.
Finally, dividing by 4 gives
