Ch 1.4 – Equations & Inequalities

Objective:

To recognize symbols, variables, and types of sentences used in algebra.

DefinitionsExpression

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: 10 + 2 > 0 10 + 2 < 20

Symbols

Equalities Inequalities

= Equals (the same) < Is less than

> Is greater than

Is less than or equal to

Is greater than or equal to

= Not equal to

≤

≥

Give three solutions to each sentence below.

1) x > 10

2) x + 3 7≤

3) 5 - x < 0

4) 2 1 3x − >

Samples: 11, 15, 34

Samples: 4, -8, 0

Samples: 6, 7, 10

Samples: 3, 4, 7

Use mental math to solve each equation.

1) x + 4 = 9

2) 5 - x = 2

3) 2x + 3 = 17

{ 5 }

{ 3 }

{ 7 }

Expressions vs. Equations

Numerical

Variable

Expressions Equations Inequalities

2 + 35(8) - 4

x + 78 - 3y

2 + 3 = 54 + 2(3) = 10

x - 4 = 1311= 3 + 2m

9 - 5 > 3

6y - 4 < 8

Sentences

Open sentences

Open sentences have solutions and can be solved.

Open sentences have solutions and can be solved.

Variable Equations Variable Inequalities

4 + m = 7 5 + y < 91- 4 - 4

m = 3

- 5 - 5

y < 86

One Solution InfiniteSolutions

Identify each as an expression, sentence, open sentence, equation, or inequality.

1) 3x + 5 = 11

2) 7 < 2(5) + 3

3) 5x - 2

4) 6m + 2 > 3

Sentence, open sentence, equation

Sentence, inequality

Expression

Sentence, open sentence, inequality