Let's first simplify the given equations:
Equation 1: 7x + 3 = 7x + 3
This equation means that for any value of x, both sides will be equal (since they have the same terms). So, it has infinite solutions.
Equation 2: 3(4x + 8) = 4(3x + 6)
Expanding both sides, we get:
12x + 24 = 12x + 24
This equation also means that for any value of x, both sides will be equal (since they have the same terms). So, it also has infinite solutions.
Now let's plug in different values of x into the original equations to show they have infinite solutions:
Example 1: x = 0
Equation 1: 7(0) + 3 = 7(0) + 3, 0 + 3 = 0 + 3, 3 = 3. True.
Equation 2: 3(4(0) + 8) = 4(3(0) + 6), 3(8) = 4(6), 24 = 24. True.
Example 2: x = 1
Equation 1: 7(1) + 3 = 7(1) + 3, 7 + 3 = 7 + 3, 10 = 10. True.
Equation 2: 3(4(1) + 8) = 4(3(1) + 6), 3(12) = 4(9), 36 = 36. True.
Example 3: x = -2
Equation 1: 7(-2) + 3 = 7(-2) + 3, -14 + 3 = -14 + 3, -11 = -11. True.
Equation 2: 3(4(-2) + 8) = 4(3(-2) + 6), 3(-8 + 8) = 4(-6 + 6), 0 = 0. True.
We can keep going with different values for x and see that the given equations always hold. Therefore, we can conclude that these equations have infinite solutions.
7x+3=7x+3 3(4x+8)=4(3x+6)
more than one point into the original equations and check to show that the equations can have more than one solution. Explain your work.
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