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Math Help - Solutions to Equations and Inequalities

  1. #1
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    Solutions to Equations and Inequalities

    My teacher is a bad explainer so I need someone else who can explain it to me again.

    I want to know what it means for a set of numbers to be a solution for an equation or inequality.

    A thorough explanation if possible please~
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  2. #2
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    Quote Originally Posted by aloha.world View Post
    My teacher is a bad explainer so I need someone else who can explain it to me again.

    I want to know what it means for a set of numbers to be a solution for an equation or inequality.

    A thorough explanation if possible please~
    If you have two or more possible solutions to an equation, then the full solution is the set of all possible solutions.

    A simple example is the quadratic equation x^2 - 5x + 6=0.

    When factorised, this gives (x-3)(x-2)=0

    and so by the null factor law

    x - 3 = 0 or x - 2 = 0

    and so x = 3 or x = 2.


    So the solution set is x = \{2, 3\}.


    Does that make sense?
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  3. #3
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    Quote Originally Posted by Prove It View Post
    If you have two or more possible solutions to an equation, then the full solution is the set of all possible solutions.

    A simple example is the quadratic equation x^2 - 5x + 6=0.

    When factorised, this gives (x-3)(x-2)=0

    and so by the null factor law

    x - 3 = 0 or x - 2 = 0

    and so x = 3 or x = 2.


    So the solution set is x = \{2, 3\}.


    Does that make sense?
    It kind of makes sense, but can you explain it in words?
    ...
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  4. #4
    Member Greengoblin's Avatar
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    There are two possible x values that make the above equation true, x=2, and x=3.

    A set is an abstract collection of objects - could be the set of all bananas, the set of all elephants, or more commonly in mathematics, a set of numbers.

    For example the set of all even numbers is written within curly parenthesis like so: \mathbb{Z}_{Even}=\{2,4,6,8,\cdots\}=\{2n:n\in\mat  hbb{Z}\}

    In this case we have the set of all solutions to the equation: {2,3}
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