Algebraic Expressions

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Algebraic Expressions
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Warm Up
Change 0.483 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