2.2 Linear Inequalities

Lesson Plan 2.2: Linear Inequalities

Objectives:

• Understanding linear inequalities graphically (on number lines) and mathematically (solving).
• Using various types of notation to represent solution sets of inequalities.
• Translating word problems to linear inequalities and solving.

Suggested Lecture Breaks:

• MWF: You have two days. Get through Problem 3 on the first day.
• MW: You have one day.
• TR: You have 1.5 days. The first (half) day, get through Problem 3.

Suggested Lecture Notes:

• Have students work on problems 1 and 2 as a warmup.

Inequalities

• Give the definition of an inequality as well as the four types of inequalities. Make sure to explain the difference between strict and nonstrict inequalities.
• Give various examples of inequalities, and practice as a class representing them in three different ways:
  • As (some expression) (inequality symbol) (some expression)
  • On a number line
  • In interval notation
• Point out to students that we put emphasis on interval notation, and that for the most part, they will be asked to give answers in that format. However, graph notation can be helpful for students to learn so that they have a picture to think about.

Solving Inequalities

• Explain to students that we can perform the same operations to solve an inequality as we would an equation.
• Show by example that when we multiply or divide an inequality by a negative number, we must "flip" the inequality symbol.
  • Example: 10 < 12 is true! But -2(10<12) => -20 < -24 is NOT true. However, -20 > -24 is true.
• Give a few examples where you have to solve for a variable in an inequality. Represent these in interval notation and on a number line.
• Have students work through Problem 3. It's worth having a discussion about 3(e).

Deciding if an Expression is Positive/Negative/Zero

• Give students a simple expression and ask how they would know that it is positive. Negative? Zero?
• Use their input to formulate a definition for them:

A number x is:

• positive if x>0
• negative if x<0
• zero if x=0

• Have students work on Problem 4.

Inequalities in Word Problems

• Remind students that we are in an inequality section, so they should take this as a hint to try to use inequalities to solve the story problems.
• You might need to help students get started on problem 5.
• Problem 6 is worthwhile to discuss as a class. Use this as an opportunity to make a point about how their grades are calculated and how important it is to come to class and do their homework.