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Notes October 8, 2012 Unit 3 Linear Expressions and Equations Expressions Linear Expressions and Equations

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How can I tell the difference? An equation has an equals sign, and an expression does not. Define expression: A statement formed with operations, numbers, and variable(s). Expressions may not contain the equal sign (=) or any type of inequality.inequality Expression or Equation?

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Define term: Parts of an expression or series separated by + or – signs, or the parts of a sequence separated by commas.expressionseriessequence Examples # of Coefficient Variable(s) Exponent(s) Constant(s) Terms 3x + 4 5y 2 + 3y – 8 11m 3 – 5m 2 + 22 121w 4 – 16w 2 Expressions

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Define Constant: A plain number that does not have a variable. It’s value never changes. Examples # of Coefficient(s) Variable(s) Exponent(s) Constant(s) Terms 3x + 42 3x one 4 5y 2 + 3y – 83 5 and 3y 2 and 1– 8 11m 3 – 5m 2 + 22 3 11 and – 5m 3 and 222 121w 4 – 16w 2 2 121 and – 16w 4 and 2 none (or zero)

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We need to use the Order of Operations to simplify expressions. If there are parentheses, use the Distributive Property. Distributive Property 5(x + 6) Multiply the x by 5 and multiply the 6 by 5. 5 (x + 6) 5(x + 6) = 5●x + 5●6 5(x + 6) = 5x + 30 Simplify Expressions

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Use the Distributive Property to simplify each expression. 1) 3(x – 8) 2) (7 – 2y)5 3) 12(13 + 4d) 4) (6 – 5k)(-4)

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Simplify Expressions Use the Distributive Property to simplify each expression. 1)3(x – 8) = 3●x – 3●8= 3x – 24 2)(7 – 2y)5 = 5●7 – 5●2●y= 35 – 10y 3)12(13 + 4d) = 12●13 + 12●4●d= 156 + 48d 4)(6 – 5k)-4 = -4●6 – 5●-4●k=- 24 + 20k

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Like Terms have identical variable parts. That means they have the same variable and the variables have the same exponent. * Are constants like terms? Collect Like Terms to simplify the expression Add, subtract, multiply, divide to combine like terms Examples: 1)2x + 5 + 8x 2)3y 2 - 11 + 5y 2 + 8 Simplify Expressions

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Examples: 1)2x + 5 + 8x 2x + 8x + 5 10x + 5 2) 3y 2 - 11 + 5y 2 + 8 3y 2 + 5y 2 – 11 + 8 8y 2 – 3 Simplify Expressions

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Evaluate Expressions To evaluate means to figure out or compute.compute When we evaluate an expression, we must substitute the given value into the expression, then compute. Example: Evaluate 5(x + 2) when x = 3 Substitute 3 in place of the x first. 5(3 + 2) Simplify using Order of Operations.. 5 (5) Do the arithmetic as it is shown. 25 Evaluate Expressions

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Evaluate. Remember, you can simplify first, then substitute, or you can substitute first, then simplify. Then do the math. 1)2x + 8, when x = 3 2)2(x + 8) when x = 3 3)4x 3 – 14 when x = 2 4)5x – 6 + 3x + 2, when x = 4 Evaluate Expressions

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Evaluate. Remember, simplify first. Then substitute. Then do the math. 1)2x + 8, when x = 3 2(3) + 8 6 + 8 14 2) 2(x + 8) when x = 3 2x + 16 2(3) + 16 6 + 16 22

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3)4x 3 – 14 when x = 2 4(2) 3 – 14 48 – 14 32 – 14 18 4)5x – 6 + 3x + 2, when x = 4 8x – 4 8(4) – 4 32 – 4 28 Evaluate Expressions

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What is an expression? How can I tell where one term starts and the next begins? Does a constant’s value ever change? What is a variable? Explain how to simplify and evaluate this example, step by step: 2x + 4(x – 5) + 18, when x = 4 Expressions Closure

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