IM: 8.4.4: More Balanced Moves (Lesson)

Here is an equation, and then all the steps Clare wrote to solve it:

14x - 2x + 3 = 3(5x + 9)

12x + 3 = 3(5x +9)

3(4x + 1) = 3(5x +9)

4x + 1 = 5x + 9

1 = x + 9

-8 = x

Here is the same equation, and the steps Lin wrote to solve it:

14x - 2x + 3 = 3(5x + 9)

12x + 3 = 3(5x +9)

12x + 3 = 15x + 27

12x = 15x + 24

-3x = 24

x = -8

Mai and Noah also solved the equation, but some of their steps have errors.

Mai:

14x - 2x +3 = 3(5x +9)

12x + 3 = 3(5x +9)

7x + 3 = 3(9)

7x + 3 = 27

7x = 24

x = 24/7

Noah:

14x - 2x +3 = 3(5x +9)

12x + 3 = 15x + 27

27x + 3 = 27

27x = 24

x = 24/27