Question

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

Answer 1

For the equation 7x+3=7x+3, we can plug in any real number for x and the equation will be true. Let's try plugging in x=0:

7(0) + 3 = 7(0) + 3
0 + 3 = 0 + 3
3 = 3

This shows that the equation is true for x=0. Let's try another value, x=1:

7(1) + 3 = 7(1) + 3
7 + 3 = 7 + 3
10 = 10

Again, the equation is true for x=1. We can continue plugging in different values for x, and in every case, the equation will be true. This shows that the equation 7x+3=7x+3 has infinitely many solutions. No matter what value we choose for x, the equation will always be true.

Now let's consider the equation 3(4x+8)=4(3x+6):

We can simplify this equation by distributing the coefficients:

12x + 24 = 12x + 24

Subtracting 12x from both sides gives:

12x - 12x + 24 = 12x - 12x + 24
24 = 24

The equation 3(4x+8)=4(3x+6) is true for any value of x. This means that there are infinitely many solutions for this equation as well.