S

Solving Linear Inequalities

CHAPTER 2

2.1 Writing and Graphing Inequalities

What you will learn: Write linear inequalities Sketch the graphs of linear

inequalities Write linear inequalities from graph

Essential Question

How can you use an inequality to describe a real-life statement?

Vocabulary

Inequality

Solution of an inequality

Solution set

Graph of an inequality

Expression

Inequality

a mathematical sentence that compares expressions

Contains the symbol <, >, ≤, or ≥

Solution of an inequality

Value that makes the inequality true

An inequality can have more than one solution.

Solution Set

The set of all solutions

Graph of an inequality

Shows the solution set of an inequality on a number line

An open circle is used when a number is NOT a solution

A closed circle is used when a number is a solution

Expression

A combination of mathematical symbols and numbers

2.2 Solving Inequalities Using Addition or Subtraction

What you will learn: Solve inequalities using

addition Solve inequalities using

subtraction Use inequalities to solve

real-life problems

Essential Question:

How can you use addition or subtraction to solve an inequality?

LEAVE 4 LINES

Previous Vocabulary

Inequality (2.1)

Vocabulary

Equivalent inequalities

Equivalent Inequalities

Inequalities that have the same solutions

Mean

The average of a set of numbers

2.3 Solving Inequalities with Multiplication and Division

What you will learn:

Solve inequalities by multiplying or dividing by positive numbers.

Solve inequalities by multiplying or dividing by negative numbers.

Use inequalities to solve real-life problems.

Essential Question:

How can you use addition or subtraction to solve an inequality?

LEAVE 4 LINES

Core Concept

Multiplication and Division Properties of Inequality Multiplying or dividing each side of an

inequality by the same positive number produces an equivalent inequality

Core Concept

Multiplication and Division Properties of Inequality

When multiplying or dividing each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed to produce an equivalent inequality.

2.4 Solving Multi-step Inequalities

What you will learn:

Solve multi-step inequalities Use multi-step inequalities to

solve real-life problems

Essential Question:

How can you solve a multi-step inequalities?

LEAVE 4 LINES

Core Concept

Solving Multi-step inequalities Simplify each side Use inverse operations to isolate the

variable Reverse the inequality symbol when

multiplying or dividing by a negative number

2.5 Solving Compound Inequalities

What you will learn:

Write and graph compound inequalities Solve compound inequalities Use compound inequalities to solve

real life problems

Essential Question

How can you use inequalities to describe intervals on the real number line?

Vocabulary

Compound inequalities

Compound inequalities

Formed by joining two inequalities with the word “and” or “or”

Core Concept

Compound inequalities “and” “and” is the intersection of the

inequalities “and” contains the solutions that

are the same in both inequalities

Core Concept

Graphing Compound inequalities “or” “or” is the union of the inequalities

the solutions “or” contains all the solutions for

both inequalities

1.5 Rewriting Equations and Formulas

What you will learn:

Rewrite literal equations Rewrite and use formulas for area Rewrite and use other common

formulas

Essential Question:

How can you use a formula for one measurement to write a formula for a different measurement?

Vocabulary

Literal equation Formula

Literal Equation

An equation that has two or more variables

You must solve for one variable in terms of another

Formula

A type of literal equation Shows how one variable is

related to one or more other variables