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Published byImogene Thornton Modified over 4 years ago

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1.4 Solving Equations

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●A variable is a letter which represents an unknown number. Any letter can be used as a variable. ●An algebraic expression contains at least one variable. Examples: a, x+5, 3y – 2z ●A verbal expression uses words to translate algebraic expressions. Example: “The sum of a number and 3” represents “ n+3. ” Review of Terms

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●An equation is a sentence that states that two mathematical expressions are equal. Example: 2x-16=18 To solve an equation means to find the value for the variable that satisfied the equation.

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Steps to Solving Equations ●Simplify each side of the equation, if needed, by distributing or combining like terms. ●Move variables to one side of the equation by using the opposite operation of addition or subtraction. ●Isolate the variable by applying the opposite operation to each side. First, use the opposite operation of addition or subtraction. Second, use the opposite operation of multiplication or division. ●Check your answer.

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Examples ● “y” is the variable. ● Add 6 to each side to isolate the variable. ● Now divide both sides by 3. ● The answer is 5. ● Check the answer by substituting it into the original equation.

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Try this... Did you get x = - 4 ? You were right!

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Equations with No Solution Some equations have no solution. That means that no value will work in place of the variable. The solution set is the empty set, {}. This is a false statement therefore the equation has no solution.

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Try this... Cross multiply to solve. Distribute and solve. This is a false statement. No Solution. {}

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Identity Equations Some equations have all real numbers as a solution. That means you can plug any number in for the variable and it will work. This is a true statement therefore the solution set is all real numbers.

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