Question

Kale begins solving the equation (6x - 3) = (6x - 4). Her work is correct and shown below. 2/3(6x - 3) = 1/2(6x - 4). When she adds 2 to both sides, the equation 4x = 3x results. Which solution will best illustrate what happens to x?

a) x increases by 2.
b) x decreases by 2.
c) x remains the same.
d) x is undefined.

Answer 1

The solution to the equation 4x = 3x illustrates that x remains the same.

Step-by-step explanation:

Kale begins solving the equation (6x - 3) = (6x - 4). Her work is correct and shown below.

2/3(6x - 3) = 1/2(6x - 4).

When she adds 2 to both sides, the equation 4x = 3x results.

To determine what happens to x, we need to look at the equation 4x = 3x.

If we subtract 3x from both sides, we get x = 0.

Therefore, the solution illustrates that x remains the same, which is option c).