G8

Copyright © Swun Math (^) Grade 8 Unit 4 Lesson 10 P TE

Input/Model

(Teacher Presents)

Directions: Simplify. Determine how many solutions.

1.

18a + 14b – 12 = 11a + 5 – 4b + 7a + 18b + 7

Solution:

• Step 1: Analyze the problem


• Step 2: Simplify the equation using inverse operations and collecting like terms to eliminate terms.
  18 푎푎 + 14 푏푏 – 12 = 11 푎푎 + 5 – 4푏푏 + 7푎푎 + 18 푏푏 + 7

18 푎푎 + 14 푏푏 – 12 = 18 푎푎 + 14 푏푏 + 12

− 12 = 12

• Step 3: Since the variables cancel out and unequal numbers remain, there is no solution.

2.

3b + 5 + 2b = 5 + 1b + 5b ─ b

Solution:

• Step 1: Analyze the problem


• Step 2: Simplify the equation using inverse operations and collecting like terms to eliminate terms.
  5b + 5 = 5 + 5b


• Step 3: Since the result is equivalent equations and will result in 1 = 1, then there are infinite solutions. I
  can see that both sides have the same exact terms; therefore, there are infinite solutions.