Learn on PengiReveal Math, AcceleratedUnit 8: Solve Problems Using Equations and Inequalities

Lesson 8-1: Write and Solve Equations: px + q = r

In this Grade 7 lesson from Reveal Math, Accelerated, students learn to write and solve two-step equations in the form px + q = r by applying Properties of Equality to isolate the variable. Using real-world contexts like marching band costs and airplane cruising time, students practice defining variables, setting up equations, and solving by performing inverse operations in the correct order. The lesson also addresses unit analysis, helping students understand how each term in an equation must represent the same unit of measurement.

Section 1

Inverse Operations

Property

Multiplication and division are opposite or inverse operations, because each operation undoes the effects of the other.
Addition and subtraction are opposite or inverse operations, because each operation undoes the effects of the other.

Examples

To undo adding 8, you subtract 8. For example, $x + 8 - 8$ simplifies back to just $x$ .
To undo multiplying by 3, you divide by 3. For example, $\frac{3y}{3}$ simplifies back to just $y$ .
The inverse of subtracting 10 is adding 10, and the inverse of dividing by 5 is multiplying by 5.

Explanation

Inverse operations are pairs of actions that cancel each other out, like locking and unlocking a door. We use them to isolate a variable by undoing whatever operation is being performed on it.

Section 2

Identifying Relationships Modeled by $px+q=r$

Property

A relationship of the form $px+q=r$ describes a situation where a total amount, $r$ , is the sum of a variable amount, $px$ , and a fixed starting amount, $q$ . The variable amount is found by multiplying a rate, $p$ , by a quantity, $x$ .

px + q = r

Section 3

Solving Equations of the Form px+q=r

Property

To solve a two-step equation of the form $px+q=r$ , we use inverse operations to isolate the variable. The goal is to find the value of $x$ that makes the equation true.

The general procedure is:

Undo the addition or subtraction of the constant term ( $q$ ).
Undo the multiplication or division by the coefficient ( $p$ ).

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Inverse Operations

Property

Examples

To undo adding 8, you subtract 8. For example, $x + 8 - 8$ simplifies back to just $x$ .
To undo multiplying by 3, you divide by 3. For example, $\frac{3y}{3}$ simplifies back to just $y$ .
The inverse of subtracting 10 is adding 10, and the inverse of dividing by 5 is multiplying by 5.

Explanation

Inverse operations are pairs of actions that cancel each other out, like locking and unlocking a door. We use them to isolate a variable by undoing whatever operation is being performed on it.

Section 2

Identifying Relationships Modeled by $px+q=r$

Property

px + q = r

Section 3

Solving Equations of the Form px+q=r

Property

To solve a two-step equation of the form $px+q=r$ , we use inverse operations to isolate the variable. The goal is to find the value of $x$ that makes the equation true.

The general procedure is:

Undo the addition or subtraction of the constant term ( $q$ ).
Undo the multiplication or division by the coefficient ( $p$ ).

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Inverse Operations

Property

Examples

To undo adding 8, you subtract 8. For example, $x + 8 - 8$ simplifies back to just $x$ .
To undo multiplying by 3, you divide by 3. For example, $\frac{3y}{3}$ simplifies back to just $y$ .
The inverse of subtracting 10 is adding 10, and the inverse of dividing by 5 is multiplying by 5.

Explanation

Inverse operations are pairs of actions that cancel each other out, like locking and unlocking a door. We use them to isolate a variable by undoing whatever operation is being performed on it.

Section 2

Identifying Relationships Modeled by $px+q=r$

Property

px + q = r

Section 3

Solving Equations of the Form px+q=r

Property

To solve a two-step equation of the form $px+q=r$ , we use inverse operations to isolate the variable. The goal is to find the value of $x$ that makes the equation true.

The general procedure is:

Undo the addition or subtraction of the constant term ( $q$ ).
Undo the multiplication or division by the coefficient ( $p$ ).