Lesson 20

Interpreting Inequalities

  • Let’s interpret the meaning of situations with phrases like “at least,” “at most,” and “up to.”

20.1: Math Talk: Solving Inequalities

Mentally solve for \(x\).

  • \(5x<10\)

  • \(10>6x-2\)

  • \(9x<5-23\)

  • \(11(x-3)<46-2\)

20.2: Checking and Graphing Inequalities

Solve each inequality. Then, check your answer using a value that makes your solution true.

  1. \(\text-2x<4\)

    1. Solve the inequality.
    2. Check your answer using a value that makes your solution true.

  2. \(3x+5>6x-4\)

    1. Solve the inequality.
    2. Check your answer using a value that makes your solution true.

  3. \(\text-3(x+1)\geq13\)

    1. Solve the inequality.
    2. Check your answer using a value that makes your solution true.

For each statement:

  • Use a number line to show which values satisfy the inequality.
  • Express the statement symbolically with an inequality.
  1. The elevator can lift up to 1,200 pounds. Let \(x\) represent the weight being lifted by the elevator.
    Blank number line 
  2. Over the course of the senator's term, her approval rating was always around 53% ranging 3% above or below that value. Let \(x\)  represent the senator’s approval rating.
    Blank number line 
  3. There's a minimum of 3 years of experience required. Let \(x\) represent the years of experience a candidate has.
    Blank number line 

20.3: Card Sort: What’s the Situation?

Your teacher will give you a set of cards that show a graph, an inequality, or a situation. Sort the cards into groups of your choosing. Be prepared to explain the meaning of your categories. Then, sort the cards into groups in a different way. Be prepared to explain the meaning of your new categories.

Summary