1. Question 37

2. Question 37 Consider the equation 3(2x + 5) = ax + b.
Find one value of a and one value of b so that there is exactly one value of x that makes the equation true.
Explain your reasoning
A = 3; b = 12
Students can use a calculator on this problem. They need to solve for different solutions types to understand what is happening.
For there to be one answer for x, the value of a can by anything other than 6. In order for there to be one solution, the slopes cannot be the same. The values can be anything. I chose to make my A value 3 and my B value 12, but the students answers might vary.
Since the slope cannot be 6, I chose for a to be 3. With b being 12, you get a solution that x = -1, which shows one solution.

3. Question 37 Part B
Find one value of a and one value of b so that there are infinitely many values of x that make the equation true.
Explain your reasoning
A = 6; b = 15
In order for there to be infinitely many solutions, the two lines have to be the same. For this to happen, a = 6 and b = 15.