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Here are a few recommended readings before getting started with this lesson.
Tiffaniqua's class is taking part in a simulated stock market project to learn about investing money. Every student starts with the same amount of money and their task is to make as much money as possible in three weeks!
Tiffaniqua invested all her money into one stock. After the first week, her stock was worth $65 more! After the second week, her stock was worth twice its value after the first week. During the last week of the project, the value of her stock fell by $50, making Tiffaniqua's stock worth $280.
When solving equations, sometimes more than one step is needed. Both the number of steps and the operations required depend on the complexity of the given equation. For example, consider the following pair of equations.
The general idea is to simplify both sides of the equation and then isolate the variable on one side of the equation. This is usually done by collecting all the variable terms on one side of the equations and combining them. Then, the operations applied to the variable are undone in reverse order.
Distribute 23
2a⋅2=a
Add terms
LHS⋅32=RHS⋅32
Commutative Property of Multiplication
ba⋅ab=1
1⋅a=a
a⋅cb=ca⋅b
Multiply
Calculate quotient
LHS+2y=RHS+2y
Commutative Property of Addition
Add terms
LHS+4=RHS+4
Add terms
LHS/5=RHS/5
Calculate quotient
Tiffaniqua and her friend Kevin are talking about the stock market project. Kevin is telling her how his investment is doing after two weeks.
Distribute 3
Multiply
Add terms
LHS+10=RHS+10
Add terms
LHS/3=RHS/3
Cross out common factors
Simplify quotient
Calculate quotient
Tearrik and Ramsha both invested the same amount in a single stock. After two weeks, they compared how their investments were doing.
It turns out that after two weeks, both investments are worth exactly the same amount of money!
LHS−34m=RHS−34m
Commutative Property of Addition
Rewrite 2m as 36m
Subtract terms
LHS+20=RHS+20
Add terms
LHS⋅23=RHS⋅23
Commutative Property of Multiplication
ba⋅ab=1
a⋅cb=ca⋅b
Multiply
Calculate quotient
Solve the given equation for the indicated variable. If necessary, round the answer to two decimal places.
Equations with linear terms may have zero, one, or infinitely many solutions. This lesson has already shown how to solve equations with one solution. Now it is time to focus on the other two possibilities.
There are three possible results when solving an equation.