3.3: Solve Equations Involving Inverse Properties of Subtraction and Multiplication
Have you ever looked at a homework problem and wondered how to solve it? Look at this situation that Henry faced.
Henry looked at the first problem on his homework page.
Even though he'd been paying attention in class, Henry had no idea how to solve this problem.
Do you know how to solve it? This is a twostep equation involving subtraction and multiplication. This Concept will teach you the steps for solving equations like this one.
Guidance
You are going to learn how to solve twostep equations with subtraction and multiplication in them. Let’s begin.
To solve a twostep equation, we will need to use more than one inverse operation. Let's take a look at how to solve a twostep equation now. When we perform inverse operations to find the value of a variable, we work to get the variable alone on one side of the equals. This is called isolating the variable. It is one strategy for solving equations. You can use isolating the variable whether you are solving onestep or twostep equations.
Solve for
Notice that there are two terms on the left side of the equation,
In the equation, 9 is subtracted from
Notice how we rewrote the problem above. Since we are adding a positive number, 9, to a number that is being subtracted from
The number 9 is the additive inverse, or opposite, of 9.
We can now use inverse operations to get the
The value of
Let’s review our steps for solving this twostep equation.
Take a few minutes to write these steps in your notebook.
Example A
Solution:
Example B
Solution:
Example C
Solution:
Now let's go back to the dilemma from the beginning of the Concept.
Here is the problem that Henry saw on his page.
To solve this problem, we can first add nine to both sides of the equation.
Now Henry can solve this as a onestep equation by dividing both sides by 14.
This is the answer to this problem.
Vocabulary
 Equation
 a mathematical statement with an equal sign where the quantity on one side of the equation is equal to the quantity on the other side.
 Variable
 a letter used to represent an unknown quantity.
 Algebraic Equation
 An equation with at least one variable in it.
 OneStep Equation
 An algebraic equation with one operation in it.
 TwoStep Equation
 An algebraic equation with two operations in it.
Guided Practice
Here is one for you to try on your own.
Eight times a number minus four is equal to ninety  two.
Write a twostep equation and solve for the missing variable.
Solution
First, walk through the words to write the equation.
Now solve the for the variable. First, add four to both sides of the equation.
Now divide both sides by 8.
This is our answer.
Video Review
[www.youtube.com/watch?v=9ITsXICV2u0 Solving TwoStep Equations]
Practice
Directions: Solve each twostep equation that has multiplication and subtraction in it.

4x−3=13 
5y−8=22 
7x−11=31 
8y−15=25 
9x−12=42 
12y−9=99 
2y−3=23 
3x−8=19 
5y−2=28 
7x−11=38 
5y−9=51 
6a−12=30 
9x−14=13 
12x−23=49 
13y−3=23 
18x−12=42
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Term  Definition 

Algebraic Equation  An algebraic equation contains numbers, variables, operations, and an equals sign. 
Equation  An equation is a mathematical sentence that describes two equal quantities. Equations contain equals signs. 
OneStep Equation  A onestep equation is an algebraic equation with one operation in it that requires one step to solve. 
TwoStep Equation  A twostep equation is an algebraic equation with two operations in it that requires two steps to solve. 
Variable  A variable is a symbol used to represent an unknown or changing quantity. The most common variables are a, b, x, y, m, and n. 
Image Attributions
Here you'll solve equations involving inverse properties of subtraction and multiplication.