# 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

1. $$\text-2x<4$$

1. Solve the inequality.
2. $$3x+5>6x-4$$

1. Solve the inequality.
3. $$\text-3(x+1)\geq13$$

1. Solve the inequality.

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.
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.
3. There's a minimum of 3 years of experience required. Let $$x$$ represent the years of experience a candidate has.

### 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.