Question

7x+3=7x+3 3(4x+8)=4(3x+6)
Plug more than one point into the original equations and check to show that the
equations can have more than one solution. Explain your work.

Answer 1

The first step is to show that the given equations are equivalent. Let's analyze the two equations:

Equation 1: 7x + 3 = 7x + 3

Equation 2: 3(4x + 8) = 4(3x + 6)

Let's simplify Equation 2:

Equation 2: 12x + 24 = 12x + 24

From this simplification, it is evident that Equation 2 is equivalent to Equation 1. Now let's plug in multiple points and check if they satisfy the equations.

Case 1: Let x = 1
7(1) + 3 = 7 + 3 = 10
So, for x = 1, the equations are equal to 10.

Case 2: Let x = 2
7(2) + 3 = 14 + 3 = 17
So, for x = 2, the equations are equal to 17.

As we can see, when the value of x was changed to different numbers, the equations still held true and were equal, showing that these equations do have more than one solution. In fact, since the equations are identical, they have infinitely many solutions. Any number that is plugged in for x will result in the same output for both equations, proving that there are infinitely many solutions.