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Understanding Equations and Solutions in Mathematics

Equations are a type of mathematical sentence that contains variables, numbers, and symbols, with the sides separated by an equal sign. The solution set consists of all values that make the equation true, using set notation within braces. Explore the concept of open sentences, domains, and solution sets with practical examples and step-by-step solving methods.

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Understanding Equations and Solutions in Mathematics

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  1. EquationsUnit 2

  2. Equation • Mathematical sentence with an equal sign. • Contains variables, numbers, and/or symbols • The sides of an equation are separated by an equal sign Example: 5x-1=9+x

  3. Open Sentence • An equation that contains variables

  4. Domain • A given set of numbers that are to be substituted in for the variable(s)

  5. Solution Set • All solutions that make the equation true • We use braces for set notation • If not solution exists, we use { } or • Known as the empty set • All solutions that make the equation true • We use braces for set notation • If not solution exists, we use { } or • Known as the empty set

  6. Example • Solve 5x-1=9 if • Read as “x belongs to the set whose numbers are 1, 2, and 3 • Steps used to solve this problem: • Create a table • Plug in values for the variable(s) • Simplify • If it is true, it is a solution; If it is false, not a solution

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