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Unit 4 - Lesson 8 - Grade 8: Illustrative Mathematics

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Last updated 2 months ago
26 Questions
Note from the author:
Grade 8 Unit 4
Lesson 8: How Many Solutions?
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 4
Lesson 8: How Many Solutions?
CC BY 2021 Illustrative Mathematics®
Lesson: How Many Solutions?

Matching Solutions (Warm Up)

Consider the unfinished equation
12(x - 3) + 18 = _________.

Match the following expressions with the number of solutions the equation would have with that expression.
1.

2.

3.

Thinking About Solutions Some More

Your teacher will give you some cards.
4.

Card #1: Solve the equation with your partner

5.

Card #2: Solve the equation with your partner

6.

Card #3: Solve the equation with your partner

7.

Card #4: Solve the equation with your partner

8.

Sort your cards into categories.

9.

Describe the defining characteristics of those categories and be prepared to share your reasoning with the class.


Make Use of Structure (Optional)

For each equation, determine whether it has no solutions, exactly one solution, or is true for all values of x (and has infinitely many solutions). If an equation has one solution, solve to find the value of x that makes the statement true.
10.


If the equation has one solution, solve to find the value of x that makes the statement true.

11.


If the equation has one solution, solve to find the value of x that makes the statement true.

12.


If the equation has one solution, solve to find the value of x that makes the statement true.

13.


If the equation has one solution, solve to find the value of x that makes the statement true.

14.


If the equation has one solution, solve to find the value of x that makes the statement true.

15.


If the equation has one solution, solve to find the value of x that makes the statement true.

16.


If the equation has one solution, solve to find the value of x that makes the statement true.

17.


If the equation has one solution, solve to find the value of x that makes the statement true.

18.


If the equation has one solution, solve to find the value of x that makes the statement true.

19.


If the equation has one solution, solve to find the value of x that makes the statement true.

20.


If the equation has one solution, solve to find the value of x that makes the statement true.

21.


If the equation has one solution, solve to find the value of x that makes the statement true.

22.


If the equation has one solution, solve to find the value of x that makes the statement true.

23.


If the equation has one solution, solve to find the value of x that makes the statement true.

24.


If the equation has one solution, solve to find the value of x that makes the statement true.

25.

What do you notice about equations with one solution? How is this different from equations with no solutions and equations that are true for every x?


Cool Down: How Does She Know?

How Does She Know?

Elena began to solve this equation:
26.

When she got to the last line she stopped and said the equation is true for all values of x. How could Elena tell?