Amsco Integrated Algebra I: Solving Equations Using More Than One Operation
 This is a free lesson from our course in Amsco's Integrated Algebra

 This lesson explains in more details using earlier learning of short terms and definitions about: an equation, (a true sentence, a false sentence or an open sentence), solution set of the open sentence. If every element of the domain satisfies an equation, the equation is called an identity. E.g. 5 + x = x- (-5) is an identity when the domain is the set of real numbers because every element of the domain makes the sentence true. An equation is a sentence that states that two algebraic expressions are equal. E.g. x + 3 = 9 is an equation in which x + 3 is called the left side, or left member, and 9 is the right side, or right member. (More text below video...)
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 (Continued from above) Two equations that have the same solution set are equivalent equations. To solve an equation is to find its solution set. If not every element of the domain makes the sentence true, the equation is called a conditional equation, or simply an equation. Therefore, x + 3 = 9 is a conditional equation. Remember properties of equality: • addition Property- If equals are added to equals, the sums are equal. • subtraction Property- If equals are subtracted from equals, the differences are equal. • multiplication Property- If equals are multiplied by equals, the products are equal. • division Property- If equals are divided by non-zero equals, the quotients are equal. • substitution Property:- In a statement of equality, a quantity may be substituted for its equal. For example: To find the solution of the equation 2x + 3 = 15, you’ll use several properties of the four basic operations and of equality. These steps and properties are necessary to justify the solution i.e. x = 6, of this equation. The video above will explain in detail with the help of several examples.

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