# Lesson 15

Solving Equations with Rational Numbers

### Lesson Narrative

The purpose of this lesson is to get students thinking about how to solve equations involving rational numbers. In grade 6, students solved equations of the form $$px=q$$ and $$x+p=q$$ and saw that additive and multiplicative inverses (opposites and reciprocals) were useful for solving them. However, that work in grade 6 did not include equations with negative values of $$p$$ or $$q$$ or with negative solutions. This lesson builds on the ideas of the last lesson and brings together the work on equations in grade 6 with the work on operations on rational numbers from earlier in grade 7.

### Learning Goals

Teacher Facing

• Explain (orally and in writing) how to solve an equation of the form $x+p=q$ or $px=q$, where $p$, $q$, and $x$ are rational numbers.
• Generalize (orally) the usefulness of additive inverses and multiplicative inverses for solving equations of the form $x+p=q$ or $px=q$.
• Generate an equation of the form $x+p=q$ or $px=q$ to represent a situation involving rational numbers.

### Student Facing

Let’s solve equations that include negative values.

### Required Preparation

Print and cut up cards from the Card Sort: Matching Inverses blackline master.  Prepare 1 set of cards for every 2 students.

### Student Facing

• I can solve equations that include rational numbers and have rational solutions.

Building On

Building Towards

### Glossary Entries

• variable

A variable is a letter that represents a number. You can choose different numbers for the value of the variable.

For example, in the expression $$10-x$$, the variable is $$x$$. If the value of $$x$$ is 3, then $$10-x=7$$, because $$10-3=7$$. If the value of $$x$$ is 6, then $$10-x=4$$, because $$10-6=4$$.

### Print Formatted Materials

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