 # 1.4 Solving Equations ●A variable is a letter which represents an unknown number. Any letter can be used as a variable. ●An algebraic expression contains.

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1.4 Solving Equations

●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

●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.

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.

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.

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

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.

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

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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