G8

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

Input/Model

(Teacher Presents)

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

1. 2b = ─7b + 9b

Solution:

• If needed, use the visual models to simplify both
  sides of the equation.


• Or, simplify both sides of the equation
  procedurally:
  ─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

2. ─4a = 8 ─ 4a

Solution:

• Visually simplify:


• Notice that you are left with nothing on left, this is
  0. You have 8 positives. So, the equation looks
  like this: 0=8; which is not true.


• Procedurally, 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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