Equivalent Equations for the Same Situation
Equivalent Equations for the Same Situation is a Grade 7 math skill in Illustrative Mathematics, Chapter 6: Expressions, Equations, and Inequalities. Students learn that a single real-world situation can be modeled by multiple equivalent equations that all have the same solution.
Key Concepts
An equation of the form $p(x+q)=r$ can be rewritten as an equivalent equation of the form $px+pq=r$ by using the distributive property. $$p(x+q) = px + pq$$.
Common Questions
What are equivalent equations?
Equivalent equations are different equations that have the same solution set. They model the same situation from different starting points or perspectives.
How can the same situation generate different equations?
Depending on which quantity you define as unknown and how you set up the relationship, you can write multiple valid equations that all solve to the same answer.
What is an example of equivalent equations for the same situation?
If total cost is $36 for 4 tickets, you could write 4x equals 36 (finding price per ticket) or x equals 36 divided by 4 (already simplified). Both represent the same situation.
How do you verify two equations are equivalent?
Solve both equations. If they have the same solution, they are equivalent. You can also manipulate one equation using algebraic properties to obtain the other.
What chapter covers equivalent equations in Illustrative Mathematics Grade 7?
Equivalent equations for the same situation are covered in Chapter 6: Expressions, Equations, and Inequalities in Illustrative Mathematics Grade 7.