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## 9.1 – Solving Equations

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**Definition: Solution**• A solution to an equation is a value for the variable that makes the equation a true statement. • To solve an equation means to find all solutions to the equation. Examples: Solve and check:**Definition: Solution**• The value of a networked color printer purchased new decreased by the same amount each year (called depreciation). After 4 years, the value of the printer dropped by $1,300. By how much did the value decrease each year? Write an equation and solve. • A car rents for $35 per day plus 30¢ per mile. How many miles were driven if the rental fee for a day was $65. Write an equation and solve.**Definition: Solution**• Like terms are terms that have the same variables with the same exponents. Terms that are not like are called unlike terms. • The coefficient of a term is the real number in front of the variable. Example: Which terms are like and which are unlike?**Combining Like Terms**• If terms are like, combine (add or subtract) their coefficients. • Keep the variable and exponent. Examples: Simplify each expression.**Solving Multistep Equations**• Apply the distributive property to eliminate grouping symbols (parentheses). • Combine like terms on either side of the equations. • Add or subtract to isolate the terms with a variable on one side of the equation and the terms without variables on the other side of the equation. • Multiply by the reciprocal of the coefficient (or divide by the coefficient) on the variable term to solve for the variable • Check your answer.**Combining Like Terms**Examples: Solve each equation. Check your answer.**Formulas**• Formulas are equations in which the variables have specific meanings in the real world. Example: Find the following quantity.