Question

Plug in x=3 and x=-2 for both of the original equations to show that the equations
can have more than one solution. Solve the equations. Explain your work.
7x + 3 = 7x + 3
3 (4x + 8) = 4 (3x + 6)
No special characters, i wnat to copy and paste

Answer 1

To determine if the equations can have more than one solution, let's first check each equation by plugging in the values of x = 3 and x = -2.

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

Let's check x = 3:

7(3) + 3 = 7(3) + 3
21 + 3 = 21 + 3
24 = 24 (True)

Now let's check x = -2:

7(-2) + 3 = 7(-2) + 3
-14 + 3 = -14 + 3
-11 = -11 (True)

Since both values satisfy the equation, it is true for all x because both sides of the equation are identical. This means that the first equation has an infinite number of solutions.

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

First, we simplify both sides of the equation.

Left side:
3(4x + 8) = 12x + 24

Right side:
4(3x + 6) = 12x + 24

Now, we have:

12x + 24 = 12x + 24

Let's check x = 3:

12(3) + 24 = 12(3) + 24
36 + 24 = 36 + 24
60 = 60 (True)

Now let's check x = -2:

12(-2) + 24 = 12(-2) + 24
-24 + 24 = -24 + 24
0 = 0 (True)

Since both x = 3 and x = -2 satisfy the equation, and we have established that the equation simplifies to an identical expression on both sides, this equation is also true for all x. In other words, it has infinitely many solutions as well.

### Conclusion:

Both equations 7x + 3 = 7x + 3 and 3(4x + 8) = 4(3x + 6) have an infinite number of solutions because they simplify to expressions that are always equal regardless of the value of x.

Thus, there are more than one solution possible; in fact, every real number is a solution for both equations.