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.
Describe some ways the steps they took are alike and different.
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
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?