# Lesson 13

Reintroducing Inequalities

### Lesson Narrative

In grade 6, students learned how to write and interpret inequalities of the form $$x < c$$ and $$x > c$$. In this lesson, students begin to investigate inequalities of the form $$px<q$$ and $$x + p < q$$.

First, they are reintroduced to the notation < and > and reminded how inequalities can be expressed algebraically and graphically on a number line. A context is used to help students make sense of inequalities. The symbols $$\leq$$ and $$\geq$$ are introduced, which are the relevant symbols to use in many of the modeling problems they will see later on. Then they use substitution to check whether given values of $$x$$ satisfy inequalities.

### Learning Goals

Teacher Facing

• Comprehend the terms “less than or equal to” and “greater than or equal to” (in spoken and written language) and the symbols ≤ and ≥ (in written language).
• Recognize that more than one value for a variable makes the same inequality true.
• Use substitution to determine whether a given value for a variable makes an inequality true, and justify (orally) the answer.

### Student Facing

Let’s work with inequalities.

### Student Facing

• I can explain what the symbols $\le$ and $\ge$ mean.
• I can represent an inequality on a number line.
• I understand what it means for a number to make an inequality true.

Building On

Building Towards