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Mathematics LibreTexts

Section 1.3

  • Page ID
    23212
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    Main difference #1:
    Linear Equations typically have 1 solution (they can have none, or an infinite amount as well).
    Linear Inequalities will typically have an infinite amount of solutions.
    Consider the inequality \(x > 5\). How many numbers do you know that would satisfy x?
    Some examples of numbers greater than 5 are: 6, 7.8, 9000, 463, etc.
    There are an infinite amount of solutions!
    Thus, when we express the solution set for an inequality, we must write it with an inequality and
    in interval notation, to show all the numbers in the solution.


    Main difference #2:
    Recall when we talked about solving linear equations, we used two properties: the additive
    property of equality, and the multiplicative property of equality. The additive property of equality
    holds for inequalities, however the multiplicative property of equality does NOT always hold for
    inequalities.
    Why? Well, let’s consider the following example: 9 > 4. If we were to multiply both side of this
    inequality by 2, will it still be true? Let’s try it: 9(2) > ? 4(2), is equal to saying 18 > 8. Sure, it's still
    true, 18 is greater than 8.