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**Algebraic Expressions**

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Warm Up Change to a Percent Simplify

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Like Terms Term- a number, variable, or product of a number and one or more variables Ex.: 3a – 4b + 5 has 3 terms Like Terms- terms with the same variables and the same exponents Ex.: 2x, 3x 4mn, 12mn In the term 3a, 3 is called the numerical coefficient Note: and are NOT like terms

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Simplify

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Simplify

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Simplify

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Solving Equations

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Solving Equations In this section we are going to learn how to solve linear (or first degree) equations. A linear equation is one in which the exponent on the variable is 1. Example: 5x – 1 = 3 2x + 4 = 6x - 5

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Equivalent Equations Equivalent Equations are equations that have the same solution. The following are equivalent equations: 2x – 5 = 1 2x = 6 x = 3

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When we solve an equation, we write the equation as a series of simpler equivalent equations until we obtain an equation of the form x = c, where c is some real number.

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Isolate the Variable To solve any equation, we have to isolate the variable. That means getting the variable by itself on one side of the equals sign. There are 4 properties we will use to isolate the variable.

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**Addition Property of Equality**

You can add the same number to both sides of an equation and the equation remains equivalent.

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Example:

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**Subtraction Property of Equality**

You can subtract the same number to both sides of an equation and the equation remains equivalent.

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Example:

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**Multiplication Property of Equality**

You can multiply the same number on both sides of an equation and the equation remains equivalent.

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Example:

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**Division Property of Equality**

You can divide the same number on both sides of an equation and the equation remains equivalent.

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Example:

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**Procedure to Solve Equations**

1. Get rid of fractions. 2. Distribute when needed. 3. Combine like terms on same side of equals. Use the addition/subtraction property. You may have to use it more than once! Solve using either the multiplication property or the division property.

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Solve

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Solve

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Solve

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**Variables on Both Sides**

Your goal is to get the variable on one side of the equals sign and everything else on the other side of the equals sign. Always combine like terms on each side of the equation FIRST!

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Example:

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Solve

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Solve

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Grouping Symbols You have to distribute before you combine like terms.

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Solve

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Solve

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