1. Ch 1.4 – Equations & Inequalities
Objective:
To recognize symbols, variables, and types of sentences used in algebra.

2. Definitions Expression
An expression involves numbers and/or variables and math operators
(+, --, *, /) and only one side of an equation.
For example: 5x + 2
Equation
A statement formed by placing an equal sign (=) between two expressions.
 For example: 5(x) + 2 = 12
Inequality
A statement formed by placing a “greater than” sign (>)
or a “less than” sign (<) between two expressions.
 For example: > < 20

3. Is greater than or equal to
Symbols
Equalities
Inequalities
<
Is less than =
Equals (the same)
>
Is greater than
Is less than or
equal to
Is greater than or equal to ≥
Not equal to =

4. 1) x > 10 Samples: 11, 15, 34 2) x + 3 7 Samples: 4, -8, 0
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: 3, 4, 7

5. Use mental math to solve each equation.
1) x + 4 = 9
{ 5 }
2) 5 - x = 2
{ 3 }
3) 2x + 3 = 17
{ 7 }

6. 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.

7. 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

8. 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