Plug more than one point into the original equations and check to show that the

Question

equations can have more than one solution. Explain your work. 7x+3=7x+3 and 3(4x+8)=4(3x+6)

Answer 1

Let's plug in two different values for x into the first equation and two different values for x into the second equation and see if they hold true.

For the first equation 7x + 3 = 7x + 3:
Let's plug in x = 1:
7(1) + 3 = 7(1) + 3
10 = 10 (True)

Now, let's plug in x = 2:
7(2) + 3 = 7(2) + 3
17 = 17 (True)

Since both values of x satisfy the equation, there are multiple solutions to this equation.

For the second equation 3(4x + 8) = 4(3x + 6):
Let's plug in x = 1:
3(4(1) + 8) = 4(3(1) + 6)
3(12) = 4(9)
36 = 36 (True)

Now, let's plug in x = 2:
3(4(2) + 8) = 4(3(2) + 6)
3(16) = 4(12)
48 = 48 (True)

Similarly, both values of x satisfy the second equation, indicating that there are multiple solutions.

In conclusion, by plugging in different values for x into both equations and checking if the equations hold true, we have shown that both equations can have more than one solution.