Lesson 6: Strategic Solving
Let’s solve linear equations like a boss.
Illustrative Math Unit 8.4, Lesson 6 (printable worksheets)
Lesson 6 Summary
Lesson 6.1 Equation Talk
The triangle and the square have equal perimeters.
- Find the value of x.
- What is the perimeter of each of the figures?
Lesson 6.2 Predicting Solutions
Without solving, identify whether these equations have a solution that is positive, negative, or zero.
Lesson 6.3 Which Would You Rather Solve?
Here are a lot of equations:
- Without solving, identify 3 equations that you think would be least difficult to solve and 3 equations you think would be most difficult to solve. Be prepared to explain your reasoning.
- Choose 3 equations to solve. At least one should be from your “least difficult” list and one should be from your “most difficult” list.
Are you ready for more?
Mai gave half of her brownies, and then half a brownie more, to Kiran. Then she gave half of what was left, and half a brownie more, to Tyler. That left her with one remaining brownie. How many brownies did she have to start with?
We can work backwards from the one remaining brownie.
(1 + 1/2) · 2 = 3
(3 + 1/2) · 2 = 7
We can check.
Mai had 7 brownies, she gave 4 brownies to Kiran and 2 brownies to Tyler.
Lesson 6 Practice Problems
- Solve each of these equations. Explain or show your reasoning.
- Solve each equation and check your solution.
- Elena said the equation 9x + 15 = 3x + 15 has no solutions because 9x is greater than 3x. Do you agree with Elena? Explain your reasoning.
- The table gives some sample data for two quantities, x and y, that are in a proportional relationship.
a. Complete the table.
b. Write an equation that represents the relationship between x and y shown in the table.
c. Graph the relationship. Use a scale for the axes that shows all the points in the table.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.