Notes October 8, 2012Unit 3 Linear Expressions and

Equations

Expressions

Linear Expressions and Equations

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.

Expression or Equation?

Define term:• Parts of an expression or series separated by + or –

signs, or the parts of a sequence separated by commas.

Examples # of Coefficient Variable(s) Exponent(s) Constant(s)

Terms

3x + 45y2 + 3y – 811m3 – 5m2 + 22

121w4 – 16w2

Expressions

ExpressionsDefine 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 + 4 2 3 x one 45y2 + 3y – 8 3 5 and 3 y 2 and 1 – 811m3 – 5m2 + 22 3 11 and – 5 m 3 and 2 22121w4 – 16w2 2 121 and – 16 w 4 and 2 none (or

zero)

• 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

Simplify Expressions

Use the Distributive Property to simplify each expression.

1) 3(x – 8)2) (7 – 2y)53) 12(13 + 4d)4) (6 – 5k)(-4)

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

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 expressionAdd, subtract, multiply, divide to combine like termsExamples:1) 2x + 5 + 8x2) 3y2 - 11 + 5y2 + 8

Simplify Expressions

Examples:1) 2x + 5 + 8x

2x + 8x + 5 10x + 5

2) 3y2 - 11 + 5y2 + 83y2 + 5y2 – 11 + 8 8y2 – 3

Simplify Expressions

Evaluate ExpressionsTo evaluate means to figure out or compute.When we evaluate an expression, we must substitute the given

value into the expression, then compute.

Example:Evaluate 5(x + 2) when x = 3Substitute 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

• Evaluate. Remember, you can simplify first, then substitute, or you can substitute first, then simplify. Then do the math.

1) 2x + 8, when x = 32) 2(x + 8) when x = 33) 4x3 – 14 when x = 24) 5x – 6 + 3x + 2, when x = 4

Evaluate Expressions

Evaluate Expressions

• Evaluate. Remember, simplify first. Then substitute. Then do the math.

1) 2x + 8, when x = 32(3) + 8 6 + 8 14

2) 2(x + 8) when x = 3 2x + 16 2(3) + 16 6 + 16

22

3) 4x3 – 14 when x = 24(2)3 – 14 4•8 – 14 32 – 14

18

4) 5x – 6 + 3x + 2, when x = 4 8x – 4

8(4) – 4 32 – 4 28

Evaluate Expressions

• 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