Lesson 3 Solving Equations Literally Practice Understanding
Compare strategies for solving linear equations and literal equations.
How is solving an equation with one variable similar to the work of solving an equation with more than one variable?
Open Up the Math: Launch, Explore, Discuss
Notice and Wonder
Solve each of the following equations for
Write a verbal description for each step of the equation-solving process used to solve the following equations for
Ready for More?
Work with a partner to revise and refine your justifications for problems 9 and 10. For example, what properties might you use to convince yourself that
Today I gained some new insights into the process for solving equations, including:
When solving literal equations, we may need to change the form of the expressions involving variables and operations. The following properties of operations justify how we might rewrite these expressions:
Properties of Addition
Properties of Multiplication
The Distributive Property
- associative property of addition or multiplication
- commutative property of addition or multiplication
- distributive property of multiplication over addition
- identity: additive, multiplicative
- inverse: additive, multiplicative
- properties of operations for numbers in the rational, real, or complex number systems
- Bold terms are new in this lesson.
In this lesson, we compared strategies for solving linear equations and literal equations and found that the processes for solving each are similar. We solve both types of equations by using inverse operations in the reverse order from the order used when evaluating the expression that involves the variable we are solving for. However, the answer to a linear equation is a number, while the answer to a literal equation is a variable or an expression. Sometimes we have to combine like terms, particularly if expressions containing the same variable occur on both sides of the equations. Properties of operations and properties of equality guide our thinking when solving equations and help us justify each step in our equation-solving process.
Perform the indicated operation on both sides of the given inequality and then decide if the new inequality you create is true or false.
Solve the equation and justify each step.