Question

Morgan, Dakota and Taylor showed their work solving the equation 7x+5x+1=73. Identify the student with the invalid first step and justify your reasoning. Morgan: 7x+5x+1=73 12x+1=73 Dakota: 7x+5x+1=73 7x+6x=73 Taylor: 7x+5x+1=73 7x+5x=72

Answer 1

As you can see, Taylor failed to add 1 to her equation. This ruins the whole first step. She also used 72 instead of 73 for the answer. Taylor is incorrect.

Answer 2

Explanation:

Given the equation solved by Morgan, Dakota and Taylor expressed as 7x+5x+1=73, to get the value of x, the valid steps are as shown;

7x+5x+1=73

take the sum of 7x and 5x

12x+ 1 = 73

subtract 1 from both sides

12x+1-1 = 73-1

12x = 72

Divide both sides by 12

12x/12 = 72/12

x = 6

Based on the calculation above, the students with invalid first step is Dakota.

Dakota added 5x with 1 to get 6x which is an invalid step because 1 is not attached to a variable x. A function cannot be added to a constant hence making his first step invalid.