Linear Expressions and Equations
Notes October 8, 2012
Unit 3 Linear Expressions and
Equations
Expressions
Expression or Equation?
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.
Expressions
Define term:
• Parts of an expression or series separated by + or – signs,
or the parts of a sequence separated by commas.
Examples
3x + 4
5y2 + 3y – 8
11m3 – 5m2 + 22
121w4 – 16w2
# of
Terms
Coefficient Variable(s) Exponent(s) Constant(s)
Expressions
Define Constant: A plain number that does not have a variable. It’s value never
changes.
Examples
3x + 4
5y2 + 3y – 8
11m3 – 5m2 + 22
121w4 – 16w2
# of
Coefficient(s)
Terms
2
3
3
2
3
5 and 3
11 and – 5
121 and – 16
Variable(s) Exponent(s) Constant(s)
x
y
m
w
one
4
2 and 1
–8
3 and 2
22
4 and 2 none (or
zero)
Simplify Expressions
• 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
Use the Distributive Property to simplify each
expression.
1)
2)
3)
4)
3(x – 8)
(7 – 2y)5
12(13 + 4d)
(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
Simplify Expressions
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) 3y2 - 11 + 5y2 + 8
Simplify Expressions
Examples:
1) 2x + 5 + 8x
2x + 8x + 5
10x + 5
2) 3y2 - 11 + 5y2 + 8
3y2 + 5y2 – 11 + 8
8y2 – 3
Evaluate Expressions
Evaluate Expressions
To 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 = 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
• 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) 4x3 – 14 when x = 2
4) 5x – 6 + 3x + 2, when x = 4
Evaluate Expressions
• 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
Evaluate Expressions
3) 4x3 – 14 when x = 2
4(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
Expressions Closure
• 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