 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