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Copyright © Swun Math Grade 8 Unit 4 Lesson 9 C TE

Homework

Unit 4 · Lesson 9: Equations: No Solution or Many

Objective: I will explore equations that have no solutions or many solutions.

Vocabulary Steps

No solution: If an equation yields a statement

that is not true, such as 2=3, then the equation

has no solution.

Infinite solutions: If an equation yields a

statement that is always true, such as 2=2, then

the equation has infinite solutions.

1. If using tiles, set up the problem.


2. Remove the same amount from each side of
   the equation.


3. Continue to simplify.


4. Decide if your answer has no solution or
   infinite solutions.

Example # 1 Example # 2

Directions: Simplify. Decide if the equation has many solutions or none.

2b = ─7b + 9b

Solution:

• Simplify both sides of the equation:
  ─7 + 9 = 2, so 2b = 2b


• Both sides are the equal sign are the same, so
  the statement is true.


• Also, since any value for b will work to create
  a true statement, there are infinite numbers
  of possibilities.
  Answer: Infinite solutions

─4a = 8 ─ 4a

Solution:

• Simplify both sides of the equation by using inverse
  operations.


• Add 4a to both sides: (4a) – 4a = 8 – 4a +(4a)


• Simplify: 0 = 8


• Since I know this to be untrue, there is no solution to
  this problem.
  Answer: No solution

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