To solve algebraic equations, you need to start by looking for the operation that is shown with the variable. The operation could be addition, subtraction, multiplication, or division. Once you have identified the operation, then you can determine its inverse.
Remember
Use the inverse of an operation to solve the equation.
The table below shows the inverses for the operations you have worked with.
Operation |
Inverse Operation |
|---|---|
Addition |
Subtraction |
Subtraction |
Addition |
Multiplication |
Division |
Division |
Multiplication |
In the slideshow below, a series of equations are examined to determine the inverse operation needed to solve. Read through each slide, answering any questions you find. Be sure that you understand how to identify the operation in an equation.
Willem is at the grocery store with his dad. They plan to make some apple pies for a family gathering. They need 15 apples in all. Willem's dad bought 8 apples. The equation \( a + 8 = 15 \) models this scenario, where \( a \) represents the number of apples they already had at home.
Identify the operation and the inverse operation in the equation \( a + 8 = 15 \).
Look at the given equation, \( a\bbox[yellow]{+} 8 = 15 \). The operation with the variable is addition.
What operation is addition's inverse?
subtraction
Willem and six of his friends are going to see the new superhero movie! They are the first people to arrive at the show.
The equation \( s - 7 = 139 \) represents the number of seats remaining in the theater after Willem and his friends sit down.
Identify the operation and the inverse operation in the equation \( s - 7 = 139 \).
The operation with the variable is highlighted here: \( s\bbox[yellow]{-} 7 = 139 \).
What is this operation and its inverse?
The operation is subtraction.
Its inverse is addition.
Willem's baseball league uses an average of 24 balls per game. Each team needs to provide a total of 720 new baseballs for the season.
The equation \( 24g = 720 \) represents this scenario, where \( g \) is the number of games each team in the league plays.
Look at the equation \( 24g = 720 \).
What operation is with the variable? How do you know?
Multiplication
When a number and a variable are together with no operational sign between them, then the operation is multiplication.
The operation that is the inverse of multiplication is division.
Willem earns experience points (xp) for each level of a video game that he successfully completes. The game has 60 levels, and he can earn a maximum of 52 xp per level.
The equation \( \frac{x}{60} = 52 \) represents this scenario. The variable \( x \) represents the maximum xp he can earn in the game.
If Willem wants to determine the maximum amount of xp he can earn in the game, what inverse operation should he use?
The expression \( \frac{x}{60} \) contains division.
Willem should multiply both sides of the equation by 60 because multiplication is the inverse of division. The number 60 is the value with the variable.
Let's Practice
Practice reading equations to determine the operation shown with the variable and its inverse in the activity below. Match the equation on the left with its inverse operation on the right.
