Which of these have the same solution as Equation 1? Be prepared to explain your reasoning.
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
1
Question 2
2.
Are both of their solutions correct? Explain your reasoning.
1
Question 3
3.
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
1
Question 4
4.
Find the incorrect step in Mai's solution and explain why it is incorrect.
1
Question 5
5.
Find the incorrect step in Noah's solution and explain why it is incorrect.
Question 6
6.
Solve this equation for x.
12 + 6x / 3 = 5 - 9 / 2
Question 7
7.
Solve this equation for x.
x - 4 = 1/3(6x - 54)
Question 8
8.
Solve this equation for x.
-(3x - 12) = 9x - 4
Are you ready for more?
Question 9
9.
I have 24 pencils and 3 cups. The second cup holds one more pencil than the first. The third holds one more than the second. How many pencils does each cup contain?
Describe some ways the steps they took are alike and different.