1. Lesson 2.1 Expressions, Equations, and Inequalities
Objective- To recognize symbols, variables, and types of sentences used in algebra.
Equalities
Inequalities
<
Is less than =
Equals- is the
same as
>
Is greater than
Congruent- same
size and shape
Is less than or
equal to ~
Approx. equal to
Similar- same
shape =
Not equal to
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

2. A variable represents an unknown value.
What is a variable?
A variable represents an unknown value.
1) 3 + ___ = 10
2) = 9
These are all
variables
3) x = 12
4) = 8
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

3. Expressions vs. Equations
Sentences
Expressions
Equations
Inequalities
2 + 3
2 + 3 = 5
9 - 5 > 3
Numerical
5(8) - 4
4 + 2(3) = 10
x + 7
x - 4 = 13
Variable
6y - 4 < 8
8 - 3y
11= 3 + 2m
Open sentences
Open sentences have solutions and can be solved.
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4. Identify each as an expression, sentence,
open sentence, equation, or inequality.
1) 3x + 5 = 11
Sentence, open sentence, equation
2) 7 < 2(5) + 3
Sentence, inequality
3) 5x - 2
Expression
4) 6m + 2 > 3
Sentence, open sentence, inequality
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

5. Variable Inequalities
Open sentences have solutions and can be solved.
Variable Equations
Variable Inequalities
4 + m = 7
5 + y < 91
m = 3
y < 86
Infinite
Solutions
One Solution
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

6. Replacement Sets x(x - 2) = 0 -2(-2 - 2) = 8 -1(-1 - 1) = 2
Replacement set- an exclusive set of numerical
values that may be used to solve an equation.
Solve the equation over the set { -2, -1, 0, 1, 2 }.
x(x - 2) = 0
Lock
Ring of Keys
Strategies
1) Look at the keys.
2) Try each key.
Must find all that work!
-2(-2 - 2) = 8 No
-1(-1 - 1) = 2 No
0(0 - 2) = 0
Yes
1(1 - 2) = -1 No
2(2 - 2) = 0
Yes
Solution: { 0, 2 }
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

7. Solve each sentence below using the
replacement set { 0, 1, 2, 3, 4, 5 }.
{ 5 }
1) x + 4 = 9
{ 3 }
2) 5 - x = 2
{ } or No Solution
3) 2x + 3 = 17 4)
{ 0, 1 }
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

8. Give three solutions to each sentence below.
1) x > 10
Samples: 11, 15, 34
2) x
Samples: 4, -8, 0
3) 5 - x < 0
Samples: 6, 7, 10 4)
Samples: 2, -1, -2
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series